Darryn Bryant's research interests are in combinatorics, specifically in graph theory and design theory.
He received his PhD from The University of Queensland in 1993. His current research projects concern fundamental open problems on graph decompositions and a new design theory-based approach to signal sampling via compressed sensing.
Journal Article: On Hamilton decompositions of infinite circulant graphs
Bryant, Darryn, Herke, Sarada, Maenhaut, Barbara and Webb, Bridget S. (2018) On Hamilton decompositions of infinite circulant graphs. Journal of Graph Theory, 88 3: 434-448. doi:10.1002/jgt.22223
Journal Article: Decompositions of complete multigraphs into cycles of varying lengths
Bryant, Darryn, Horsley, Daniel, Maenhaut, Barbara and Smith, Benjamin R. (2018) Decompositions of complete multigraphs into cycles of varying lengths. Journal of Combinatorial Theory Series B, 129 79-106. doi:10.1016/j.jctb.2017.09.005
Journal Article: On Hamilton decompositions of line graphs of non-hamiltonian graphs and graphs without separating transitions
Bryant, Darryn, Maenhaut, Barbara and Smith, Benjamin R. (2018) On Hamilton decompositions of line graphs of non-hamiltonian graphs and graphs without separating transitions. Australasian Journal of Combinatorics, 71 3: 537-543.
Matchings in Combinatorial Structures (ARC Discovery Project administered by Monash University)
(2015–2019) Monash University
Decompositions of graphs into cycles
(2015–2018) Vice-Chancellor's Senior Research Fellowship
The Oberwolfach Problem and related Graph Factorisations
(2015–2018) ARC Discovery Projects
Path decomposition of graphs
Doctor Philosophy
(2014) Doctor Philosophy
Some results on decompositions of circulant graphs and embeddings of partial cycle systems
(2011) Doctor Philosophy
Hamilton cycle decompositions of Cayley graphs and related topics
There is an unsolved conjecture that every connected 2k-regular Cayley graph on a finite abelian group has a decomposition into k Hamilton cycles. Cayley graphs are graphs based on groups and students who like group theory or graph theory will enjoy working on this and related problems.
The 2-factorisation problem for complete graphs
This project examines the existence of 2-factorisations of complete graphs in which the 2-factors are isomorphic to given 2-regular graphs. Using computers the problem has been completely solved for complete graphs of order less than 20 and several infinite families of results are known. However much work remains to be done on this problem and there is plenty of scope for new discoveries to be made by students who enjoy design theory or graph theory.
Bryant, D. E. and Rodger, C. (2007). Cycle decompositions. In Colbourn, C. J. and Dinitz, J. H. (Ed.), Handbook of Combinatorial Designs 2nd ed. (pp. 373-382) New York: Chapman & Hall/CRC.
Bryant, D. E. and El-Zanati, S. (2007). Graph Decompositions. In Colbourn, C. J. and Dinitz, J. H. (Ed.), Handbook of Combinatorial Designs 2nd ed. (pp. 477-486) New York: Chapman & Hall/CRC.
Keith, J. M., Hawkes D. B., Carter, J. C., Cochran, D. A. E., Adams, P., Bryant, D. E. and Mitchelson, K. R. (2007). Sequencing aided by mutagenesis facilitates the de novo sequencing of megabase DNA fragments by short read lengths. In Mitchelson, K. R. (Ed.), New High Throughput Technologies for DNA Sequencing and Genomics (pp. 303-326) Netherlands: Elsevier. doi:10.1016/S1871-0069(06)02010-6
Sequencing by Aligning Mutated DNA Fragments (SAM)
Cochran, Duncan, Lala, Gita, Keith, Jonathan, Adams, Peter, Bryant, Darryn and Mitchelson, Keith (2006). Sequencing by Aligning Mutated DNA Fragments (SAM). In Wan-Li, Xing and Jing, Cheng (Ed.), The Frontiers of Biochip Technology (pp. 231-245) New York: Springer Science+Business Media.
On Hamilton decompositions of infinite circulant graphs
Bryant, Darryn, Herke, Sarada, Maenhaut, Barbara and Webb, Bridget S. (2018) On Hamilton decompositions of infinite circulant graphs. Journal of Graph Theory, 88 3: 434-448. doi:10.1002/jgt.22223
Decompositions of complete multigraphs into cycles of varying lengths
Bryant, Darryn, Horsley, Daniel, Maenhaut, Barbara and Smith, Benjamin R. (2018) Decompositions of complete multigraphs into cycles of varying lengths. Journal of Combinatorial Theory Series B, 129 79-106. doi:10.1016/j.jctb.2017.09.005
Bryant, Darryn, Maenhaut, Barbara and Smith, Benjamin R. (2018) On Hamilton decompositions of line graphs of non-hamiltonian graphs and graphs without separating transitions. Australasian Journal of Combinatorics, 71 3: 537-543.
Steiner triple systems with high chromatic index
Bryant, Darryn, Colbourn, Charles J., Horsley, Daniel and Wanless, Ian M. (2017) Steiner triple systems with high chromatic index. SIAM Journal on Discrete Mathematics, 31 4: 2603-2611. doi:10.1137/17M1114338
Compressed sensing with combinatorial designs: theory and simulations
Bryant, Darryn, Colbourn, Charles J., Horsley, Daniel and Cathain, Padraig O. (2017) Compressed sensing with combinatorial designs: theory and simulations. IEEE Transactions On Information Theory, 63 8: 4850-4859. doi:10.1109/TIT.2017.2717584
On almost-regular edge colourings of hypergraphs
Bryant, Darryn (2016) On almost-regular edge colourings of hypergraphs. Electronic Journal of Combinatorics, 23 4: .
Decompositions of complete graphs into bipartite 2-regular subgraphs
Bryant, Darryn, Burgess, Andrea and Danziger, Peter (2016) Decompositions of complete graphs into bipartite 2-regular subgraphs. Electronic Journal of Combinatorics, 23 2: .
On factorisations of complete graphs into circulant graphs and the Oberwolfach problem
Alspach, Brian, Bryant, Darryn, Horsley, Daniel, Maenhaut, Barbara and Scharaschkin, Victor (2016) On factorisations of complete graphs into circulant graphs and the Oberwolfach problem. Ars Mathematica Contemporanea, 11 1: 157-173.
Vertex-transitive graphs that have no Hamilton decomposition
Bryant, Darryn and Dean, Matthew (2015) Vertex-transitive graphs that have no Hamilton decomposition. Journal of Combinatorial Theory. Series B, 114 237-246. doi:10.1016/j.jctb.2015.05.007
An asymptotic existence result on compressed sensing matrices
Bryant, Darryn and Catháin, Padraig Ó. (2015) An asymptotic existence result on compressed sensing matrices. Linear Algebra and Its Applications, 475 134-150. doi:10.1016/j.laa.2015.02.010
Bipartite 2-factorizations of complete multipartite graphs
Bryant, Darryn, Danziger, Peter and Pettersson, William (2015) Bipartite 2-factorizations of complete multipartite graphs. Journal of Graph Theory, 78 4: 287-294. doi:10.1002/jgt.21806
Steiner Triple Systems Without Parallel Classes
Bryant, Darryn and Horsley, Daniel (2015) Steiner Triple Systems Without Parallel Classes. Siam Journal On Discrete Mathematics, 29 1: 693-696. doi:10.1137/140996999
Decomposing graphs of high minimum degree into 4-cycles
Bryant, Darryn and Cavenagh, Nicholas J. (2014) Decomposing graphs of high minimum degree into 4-cycles. Journal of Graph Theory, 79 3: 167-177. doi:10.1002/jgt.21816
Brushing without capacity restrictions
Bryant, Darryn, Francetic, Nevena, Gordinowicz, Przemysław, Pike, David A. and Pralat, Paweł (2014) Brushing without capacity restrictions. Discrete Applied Mathematics, 170 33-45. doi:10.1016/j.dam.2014.01.024
Cycle decompositions V: complete graphs into cycles of arbitrary lengths
Bryant, Darryn, Horsley, Daniel and Pettersson, William (2014) Cycle decompositions V: complete graphs into cycles of arbitrary lengths. Proceedings of the London Mathematical Society, 108 5: 1153-1192. doi:10.1112/plms/pdt051
Decompositions of complete 3-uniform hypergraphs into small 3-uniform hypergraphs
Bryant, Darryn, Herke, Sarada, Maenhaut, Barbara and Wannasit, Wannasiri (2014) Decompositions of complete 3-uniform hypergraphs into small 3-uniform hypergraphs. Australasian Journal of Combinatorics, 60 2: 227-254.
Vertex-transitive graphs of prime-squared order are Hamilton-decomposable
Alspach, Brian, Bryant, Darryn and Kreher, Donald L. (2014) Vertex-transitive graphs of prime-squared order are Hamilton-decomposable. Journal of Combinatorial Designs, 22 1: 12-25. doi:10.1002/jcd.21381
A second infinite family of Steiner triple systems without almost parallel classes
Bryant, Darryn and Horsley, Daniel (2013) A second infinite family of Steiner triple systems without almost parallel classes. Journal of Combinatorial Theory, Series A, 120 7: 1851-1854. doi:10.1016/j.jcta.2013.07.002
On the Hamilton-Waterloo problem for bipartite 2-factors
Bryant, Darryn, Danziger, Peter and Dean, Matthew (2013) On the Hamilton-Waterloo problem for bipartite 2-factors. Journal of Combinatorial Designs, 21 2: 60-80. doi:10.1002/jcd.21312
Decomposing the complete graph into dodecahedra
Adams, P., Bryant, D. E., Forbes, A. D. and Griggs, T. S. (2012) Decomposing the complete graph into dodecahedra. Journal of Statistical Planning and Inference, 142 5: 1040-1046. doi:10.1016/j.jspi.2011.11.001
Small embeddings for partial triple systems of odd index
Bryant, Darryn and Martin, Geoffrey (2012) Small embeddings for partial triple systems of odd index. Journal of Combinatorial Theory: Series A, 119 2: 283-309. doi:10.1016/j.jcta.2011.09.008
Paley graphs have Hamilton decompositions
Alspach, Brian, Bryant, Darryn and Dyer, Danny (2012) Paley graphs have Hamilton decompositions. Discrete Mathematics, 312 1: 113-118. doi:10.1016/j.disc.2011.06.003
Bryant, Darryn, Cavenagh, Nicholas J., Maenhaut, Barbara, Pula, Kyle and Wanless, Ian M. (2012) Nonextendible Latin Cuboids. Siam Journal on Discrete Mathematics, 26 1: 239-249. doi:10.1137/110825534
On the non-existence of pair covering designs with at least as many points as blocks
Bryant, Darryn, Buchanan, Melinda, Horsley, Daniel, Maenhaut, Barbara and Scharaschkin, Victor (2011) On the non-existence of pair covering designs with at least as many points as blocks. Combinatorica, 31 5: 507-528. doi:10.1007/s00493-011-2639-y
On bipartite 2-factorizations of K(n)-I and the Oberwolfach problem
Bryant, Darryn and Danziger, Peter (2011) On bipartite 2-factorizations of K(n)-I and the Oberwolfach problem. Journal of Graph Theory, 68 1: 22-37. doi:10.1002/jgt.20538
On the existence and embedding of edge-coloured graph decompositions
Brier, Robert and Bryant, Darryn (2011) On the existence and embedding of edge-coloured graph decompositions. Ars Combinatoria, 99 445-459.
Cycle Decompositions of Complete Multigraphs
Bryant, D, Horsley, D, Maenhaut, B and Smith, BR (2011) Cycle Decompositions of Complete Multigraphs. Journal of Combinatorial Designs, 19 1: 42-69. doi:10.1002/jcd.20263
An asymptotic solution to the cycle decomposition problem for complete graphs
Bryant, Darryn and Horsley, Daniel (2010) An asymptotic solution to the cycle decomposition problem for complete graphs. Journal of Combinatorial Theory Series A, 117 8: 1258-1284. doi:10.1016/j.jcta.2010.03.015
Tran, Tran T., Kulis, Christina, Long, Steven M., Bryant, Darryn, Adams, Peter and Smythe, Mark L. (2010) Defining scaffold geometries for interacting with proteins: Geometrical classification of secondary structure linking regions. Journal of Computer-Aided Molecular Design, 24 11: 917-934. doi:10.1007/s10822-010-9384-y
Decompositions of complete graphs into long cycles
Bryant, Darryn and Horsley, Daniel (2010) Decompositions of complete graphs into long cycles. Bulletin of the London Mathematical Society, 41 5: 927-934. doi:10.1112/blms/bdp069
Packing paths in complete graphs
Bryant, Darryn (2010) Packing paths in complete graphs. Journal of Combinatorial Theory, Series B, 100 2: 206-215. doi:10.1016/j.jctb.2009.08.004
Complete solutions to the Oberwolfach problem for an infinite set of orders
Bryant, Darryn and Scharaschkin, Victor (2009) Complete solutions to the Oberwolfach problem for an infinite set of orders. Journal of Combinatorial Theory, Series B, 99 6: 904-918. doi:10.1016/j.jctb.2009.03.003
Bryant, D. (2009) Completing partial commutative quasigroups constructed from partial Steiner triple systems is NP-complete. Discrete Mathematics, 309 14: 4700-4704. doi:10.1016/j.disc.2008.05.037
Indivisible plexes in latin squares
Bryant, D., Egan, J., Maenhaut, B. and Wanless, I. M. (2009) Indivisible plexes in latin squares. Designs, Codes and Cryptography, 52 1: 93-105. doi:10.1007/s10623-009-9269-z
The nonexistence of a (K6-e)-decomposition of the complete graph K29
Hartke, S. G., Ostergard, P. R. J., Bryant, D. and El-Zanati, S. I. (2009) The nonexistence of a (K6-e)-decomposition of the complete graph K29. Journal of Combinatorial Designs, 18 2: 94-104. doi:10.1002/jcd.20226
Perpendicular Rectangular Latin Arrays
Brier, Robert and Bryant, Darryn (2009) Perpendicular Rectangular Latin Arrays. Graphs and Combinatorics, 25 1: 15-25. doi:10.1007/s00373-008-0822-8
The spectrum for quasigroups with cyclic automorphisms and additional symmetries
Bryant, D., Buchanan, M. and Wanless, I. M. (2009) The spectrum for quasigroups with cyclic automorphisms and additional symmetries. Discrete Mathematics, 309 4: 821-833. doi:10.1016/j.disc.2008.01.020
A proof of Lindner's conjecture on embeddings of partial steiner triple systems
Bryant, D. and Horsley, D. (2009) A proof of Lindner's conjecture on embeddings of partial steiner triple systems. Journal of Combinatorial Designs, 17 1: 63-89. doi:10.1002/jcd.20189
Some results on decompositions of low degree circulant graphs
Bryant, Darryn and Martin, Geoffrey (2009) Some results on decompositions of low degree circulant graphs. Australasian Journal of Combinatorics, 45 251-261.
Completing partial Latin squares with two filled rows and two filled columns
Adams, Peter, Bryant, Darryn and Buchanan, Melinda (2008) Completing partial Latin squares with two filled rows and two filled columns. The Electronic Journal of Combinatorics, 15 1: Article Number: R56.
A survey on the existence of G-designs
Adams, P., Bryant, D. E. and Buchanan, M. J. (2008) A survey on the existence of G-designs. Journal of Combinatorial Designs, 16 5: 373-410. doi:10.1002/jcd.20170
Almost regular edge colorings and regular decompositions of complete graphs
Bryant, D. and Maenhaut, B. (2008) Almost regular edge colorings and regular decompositions of complete graphs. Journal of Combinatorial Designs, 16 6: 499-506. doi:10.1002/jcd.20190
Packing cycles in complete graphs
Bryant, D. E. and Horsley, D. (2008) Packing cycles in complete graphs. Journal of Combinatorial Theory, Series B, 98 5: 1014-1037. doi:10.1016/j.jctb.2007.12.004
Cycle decompositions of complete graphs
Bryant, D. E. (2007) Cycle decompositions of complete graphs. Surveys in Combinatorics 2007, London Mathematical Society Lecture Note Series, 346 67-97.
Embedding partial totally symmetric quasigroups
Bryant, D. E. and Buchanan, M. J. (2007) Embedding partial totally symmetric quasigroups. Journal of Combinatorial Theory, Series A, 114 6: 1046-1088. doi:10.1016/j.jcta.2006.10.009
Some equitably 2-colourable cycle decompositions
Adams, P., Bryant, D. E. and Waterhouse, M. A. (2007) Some equitably 2-colourable cycle decompositions. Ars Combinatoria, 85 49-64.
Star factorizations of graph products (vol 36, pg 59, 2001)
Bryant, Darryn E., El-Zanati, Saad I. and Eynden, Charles Vanden (2007) Star factorizations of graph products (vol 36, pg 59, 2001). Journal of Graph Theory, 54 1: 88-89. doi:10.1002/jgt.20213
Edge-coloured cube decompositions
Adams, Peter, Bryant, Darryn E. and Jordon, Heather (2006) Edge-coloured cube decompositions. Aequationes Mathematicae, 72 3: 213-224. doi:10.1007/s00010-006-2826-x
New families of atomic Latin squares and perfect 1-factorisations
Bryant, Darryn, Maenhaut, Barbara and Wanless, Ian M. (2006) New families of atomic Latin squares and perfect 1-factorisations. Journal of Combinatorial Theory Series A, 113 4: 608-624. doi:10.1016/j.jcta.2005.05.003
The Embedding Problem for Partial Steiner Triple Systems
Bryant, Darryn and Horsley, Daniel (2006) The Embedding Problem for Partial Steiner Triple Systems. Gazette of the Australian Mathematical Society, 33 2: 111-115.
Diagonally switchable 4-cycle systems
Adams, Peter, Bryant, Darryn, Grannell, Mike and Griggs, Terry (2006) Diagonally switchable 4-cycle systems. Australasian Journal of Combinatorics, 34 145-152.
Decomposition of complete graphs into 5-cubes
Bryant, D, El-Zanati, SI, Maenhaut, B and Vanden Eynden, C (2006) Decomposition of complete graphs into 5-cubes. Journal of Combinatorial Designs, 14 2: 159-166. doi:10.1002/jcd.20066
Steiner triple systems with two disjoint subsystems
Bryant, D and Horsley, D (2006) Steiner triple systems with two disjoint subsystems. Journal of Combinatorial Designs, 14 1: 14-24. doi:10.1002/jcd.20071
Two-factorisations of complete graphs of orders fifteen and seventeen
Adams, Peter and Bryant, Darryn (2006) Two-factorisations of complete graphs of orders fifteen and seventeen. Australasian Journal of Combinatorics, 35 1: 113-118.
Varieties of algebras arising from K-perfect m-cycle systems
Brier, R and Bryant, D (2006) Varieties of algebras arising from K-perfect m-cycle systems. Discrete Mathematics, 306 17: 2038-2046. doi:10.1016/j.disc.2006.04.002
Sampling phylogenetic tree space with the generalized Gibbs sampler
Keith, J. M., Adams, P., Ragan, M. A. and Bryant, D. E. (2005) Sampling phylogenetic tree space with the generalized Gibbs sampler. Molecular Phylogenetics and Evolution, 34 3: 459-468. doi:10.1016/j.ympev.2004.11.016
Decompositions into 2-regular subgraphs and equitable partial cycle decompositions
Bryant, D., Horsley, D. and Maenhaut, B. (2005) Decompositions into 2-regular subgraphs and equitable partial cycle decompositions. Journal of Combinatorial Theory, Series B, 93 1: 67-72. doi:10.1016/j.jctb.2004.06.002
Hamilton decompositions of complete bipartite graphs with a 3-factor leave
Bryant, D. E., Leach, C D and Rodger, C A (2005) Hamilton decompositions of complete bipartite graphs with a 3-factor leave. Australasian Journal of Combinatorics, 31 331-336.
Large sets of cycle systems on nine points
Bryant, D. E., Grannell, M. and Griggs, T. (2005) Large sets of cycle systems on nine points. Journal of Combinatorial Mathematics and Combinatorial Computing, 53 95-102.
Keith, Jonathan M., Kroese, Dirk P. and Bryant, Darryn (2004) A generalized Markov sampler. Methodology And Computing In Applied Probability, 6 1: 29-53. doi:10.1023/B:MCAP.0000012414.14405.15
Unlocking hidden genomic sequence
Keith, Jonathan M., Cochran, Duncan A. E., Lala, Gita H., Adams, Peter, Bryant, Darryn and Mitchelson, Keith R. (2004) Unlocking hidden genomic sequence. Nucleic Acids Research, 32 3: e35. doi:10.1093/nar/gnh022
Algorithms for sequence analysis via mutagenesis
Jonathan M. Keith, Peter Adams, Darryn Bryant, Duncan A. E. Cochran, Gita H. Lala and Keith R. Mitchelson (2004) Algorithms for sequence analysis via mutagenesis. Bioinformatics, 20 15: 2401-2410. doi:10.1093/bioinformatics/bth258
Common multiples of complete graphs and a 4-cycle
Adams, P, Bryant, D and Maenhaut, B (2004) Common multiples of complete graphs and a 4-cycle. Discrete Mathematics, 275 1-3: 289-297. doi:10.1016/j.disc.2002.11.001
Configurations in 4-cycle systems
Bryant, D, Grannell, M, Griggs, T and Macaj, M (2004) Configurations in 4-cycle systems. Graphs And Combinatorics, 20 2: 161-179. doi:10.1007/s00373-004-0553-4
Cube factorizations of complete graphs
Adams, P, Bryant, D and Maenhaut, B (2004) Cube factorizations of complete graphs. Journal of Combinatorial Designs, 12 5: 381-388. doi:10.1002/jcd.20015
Decompositions of complete graphs into triangles and Hamilton cycles
Bryant, Darryn and Maenhaut, Barbara (2004) Decompositions of complete graphs into triangles and Hamilton cycles. Journal of Combinatorial Designs, 12 3: 221-232. doi:10.1002/jcd.10063
Embeddings of partial Steiner triple systems
Bryant, D. E. (2004) Embeddings of partial Steiner triple systems. Journal of Combinatorial Theory Series A, 106 1: 77-108. doi:10.1016/j.jcta.2004.01.004
Existence and embeddings of partial Steiner triple systems of order ten with cubic leaves
Bryant, D., Maenhaut, B., Quinn, K. and Webb, B. S. (2004) Existence and embeddings of partial Steiner triple systems of order ten with cubic leaves. Discrete Mathematics, 284 1-3: 83-95. doi:10.1016/j.disc.2004.01.009
Hamilton cycle rich two-factorizations of complete graphs
Bryant, D (2004) Hamilton cycle rich two-factorizations of complete graphs. Journal of Combinatorial Designs, 12 2: 147-155. doi:10.1002/jcd.20005
On the completion of Latin rectangles to symmetric Latin squares
Bryant, D. and Rodger, C. A. (2004) On the completion of Latin rectangles to symmetric Latin squares. Journal of The Australian Mathematical Society, 76 1: 109-124. doi:10.1017/S1446788700008739
Some equitably 3-colourable cycle decompositions
Adams, P, Bryant, D, Lefevre, J and Waterhouse, M (2004) Some equitably 3-colourable cycle decompositions. Discrete Mathematics, 284 1-3: 21-35. doi:10.1016/j.disc.2003.11.019
Virtual drug discovery using graph
Adams, P., Bryant, D. E., Long, S., Smythe, M. L. and Tran, T. T. (2004) Virtual drug discovery using graph. Bulletin of the Institute of Combinatorics and its Applications, 40 100-106.
Common multiples of complete graphs
Bryant, Darryn and Maenhaut, Barbara (2003) Common multiples of complete graphs. Proceedings of the London Mathematical Society, 86 2: 302-326. doi:10.1112/S0024611502013771
Factorizations of the complete graph into C-5-factors and 1-factors
Adams, P, Bryant, D, El-Zanati, SI and Gavlas, H (2003) Factorizations of the complete graph into C-5-factors and 1-factors. Graphs And Combinatorics, 19 3: 289-296. doi:10.1007/s00373-002-0509-5
Inferring an original sequence from erroneous copies: two approaches
Keith, J. M., Adams, P., Bryant, D. E., Mitchelson, K. R., Cochran, D.A.E. and Lala, G. H. (2003) Inferring an original sequence from erroneous copies: two approaches. Asia-Pacific Biotech News: Special Issue: Bioinformatics in Asia Pacific, 7 3: 107-114.
Large sets of large sets of Steiner triple systems of order 9
Bryant, D., Grannell, M. and Griggs, T. (2003) Large sets of large sets of Steiner triple systems of order 9. Utilitas Mathematica, 64 115-118.
Least common multiples of cubes
Adams, P., Bryant, D. E., El-Zanati, S. I., Vanden Eynden, C. and Maenhaut, B. (2003) Least common multiples of cubes. Bulletin of the Institute of Combinatorics and its Applications, 38 45-49.
On the volume of 4-cycle trades
Bryant, D., Grannell, M., Griggs, T. and Maenhaut, B. (2003) On the volume of 4-cycle trades. Graphs And Combinatorics, 19 1: 53-63. doi:10.1007/s00373-002-0484-x
Skolem-type difference sets for cycle systems
Bryant, D., Gavlas, H. and Ling, A. C. H. (2003) Skolem-type difference sets for cycle systems. Electronic Journal of Combinatorics, 10 1: .
A family of perfect factorisations of complete bipartite graphs
Bryant, Darryn, Maenhaut, Barbara M. and Wanless, Ian M. (2002) A family of perfect factorisations of complete bipartite graphs. Journal of Combinatorial Theory Series A, 98 2: 328-342. doi:10.1006/jcta.2001.3240
Tran, T. T., Bryant, D. E. and Smythe, M. L. (2002) A subset-oriented algorithm for minimizing the number of steps required for synthesis of cyclic-peptide libraries. Computers and Chemistry, 26 2: 113-117. doi:10.1016/S0097-8485(01)00087-0
A conjecture on small embeddings of partial Steiner triple systems
Bryant, D (2002) A conjecture on small embeddings of partial Steiner triple systems. Journal of Combinatorial Designs, 10 5: 313-321. doi:10.1002/jcd.10017
A simulated annealing algorithm for finding consensus sequences
Keith, Jonathan M., Adams, Peter, Bryant, Darryn, Kroese, Dirk P., Mitchelson, Keith R., Cochran, Duncan A. E. and Lala, Gita H. (2002) A simulated annealing algorithm for finding consensus sequences. Bioinformatics, 18 11: 1494-1499. doi:10.1093/bioinformatics/18.11.1494
Tran, Tran Trung, Bryant, Darryn and Smythe, Mark (2002) A subset-orientated algorithm for minimizing the number of steps required for synthesis of cyclic-peptide libraries. Computers & chemistry, 26 2: 113-7.
Another quick proof that K10 P + P + P
Bryant, D. E. (2002) Another quick proof that K10 P + P + P. Bulletin of the Institute of Combinatorics and its Applications, 34 86-86.
Bryant, DE and Fu, HL (2002) C4-saturated bipartite graphs. Discrete Mathematics, 259 1-3: 263-268. doi:10.1016/S0012-365X(02)00371-0
Decompositions of the complete graph into small 2-regular graphs
Adams, P., Bryant, D. E. and Gavlas, H. (2002) Decompositions of the complete graph into small 2-regular graphs. Journal of Combinatorial Mathematics and Combinatorial Computing, 43 135-146.
Factorizations of and by powers of complete graphs
Bryant, D. E., El-Zanati, S. I. and Vanden Eynden, C. (2002) Factorizations of and by powers of complete graphs. Discrete Mathematics, 243 1-3: 201-205. doi:10.1016/S0012-365X(01)00216-3
On the Hamilton-Waterloo problem
Adams, P, Billington, EJ, Bryant, DE and El-Zanati, SI (2002) On the Hamilton-Waterloo problem. Graphs And Combinatorics, 18 1: 31-51. doi:10.1007/s003730200001
On the possible volumes of mu-way latin trades
Adams, P., Billington, E. J., Bryant, D. E. and Mahmoodian, E. (2002) On the possible volumes of mu-way latin trades. Aequationes Mathematicae, 63 3: 303-320.
Orthogonal quasigroups associated with m-cycle systems
Bryant, D. E. and Khodkar, A. (2002) Orthogonal quasigroups associated with m-cycle systems. Bulletin of the Institute of Combinatorics and its Applications, 36 109-112.
The three-way intersection problem for latin squares
Adams, P, Billington, EJ, Bryant, DE and Mahmoodian, ES (2002) The three-way intersection problem for latin squares. Discrete Mathematics, 243 1-3: 1-19. doi:10.1016/S0012-365X(00)00454-4
Two-dimensional balanced sampling plans excluding contiguous units
Bryant, D. E., Chang, Y. X., Rodger, C. A. and Wei, R. (2002) Two-dimensional balanced sampling plans excluding contiguous units. Communications In Statistics-theory And Methods, 31 8: 1441-1455. doi:10.1081/STA-120006078
Bryant, Darryn E., El-Zanati, Saad, Vanden Eynden, Charles and Hoffman, Dean G. (2001) Star decompositions of cubes. Graphs Combin, 17 1: 55-59. doi:10.1007/s003730170054
Bryant, D. E. (2001) 5-cycle system of l (K v-K w). Journal of Combinatorial Mathematics and Combinatorial Computing, 38 161-175.
Applications of graph theory in DNA sequencing by hybridization
Adams, P., Bryant, D. E. and Byrnes, S. (2001) Applications of graph theory in DNA sequencing by hybridization. Bulletin of the Institute of Combinatorics and its Applications, 31 13-20.
On the Oberwolfach problem with two similar length cycles
Bryant, DE (2001) On the Oberwolfach problem with two similar length cycles. Graphs And Combinatorics, 17 2: 199-206. doi:10.1007/s003730170033
On the intersection problem for 1-factorizations and near 1-factorizations of K-v
Bryant, DE and Khodkar, A (2001) On the intersection problem for 1-factorizations and near 1-factorizations of K-v. Utilitas Mathematica, 60 209-218.
Star factorizations of graph products
Bryant, DE, El-Zanati, SI and Vanden Eynden, C (2001) Star factorizations of graph products. Journal of Graph Theory, 36 2: 59-66. doi:10.1002/1097-0118(200102)36:2<59::AID-JGT1>3.0.CO;2-A
The m-way intersection problem for cubes
Adams, P. and Bryant, D. E. (2001) The m-way intersection problem for cubes. Australas. J. Combin., 23 87-100.
The mu-way intersection problem for m-cycle systems
Adams, P, Billington, EJ, Bryant, DE and Khodkar, A (2001) The mu-way intersection problem for m-cycle systems. Discrete Mathematics, 231 1-3: 27-56. doi:10.1016/S0012-365X(00)00303-4
Encoding combinatorial libraries: A novel application of fluorescent silica colloids
Grondahl, Lisbeth, Battersby, Bronwyn J., Bryant, Darryn and Trau, Matt (2000) Encoding combinatorial libraries: A novel application of fluorescent silica colloids. Langmuir, 16 25: 9709-9715. doi:10.1021/la000995z
The line structure of balanced ternary designs with block size three, index three and rho(2) = 1, 2
Adams, P., Bryant, D. E. and Khodkar, A. (2000) The line structure of balanced ternary designs with block size three, index three and rho(2) = 1, 2. Ars Combinatoria, LVI 299-308.
Maximum packings of K-v-K-u with triples
Bryant, D. E. and Khodkar, A. (2000) Maximum packings of K-v-K-u with triples. Ars Combinatoria, 55 259-270.
Toward larger chemical libraries: Encoding with fluorescent colloids in combinatorial chemistry
Battersby, Bronwyn J., Bryant, Darryn, Meutermans, Wim, Matthews, Daniel, Smythe, Mark L. and Trau, Matt (2000) Toward larger chemical libraries: Encoding with fluorescent colloids in combinatorial chemistry. Journal of the American Chemical Society, 122 9: 2138-2139. doi:10.1021/ja993634i
Maximal sets of Hamilton cycles in Kn,n
Bryant, DE, El-Zanati, S and Rodger, CA (2000) Maximal sets of Hamilton cycles in Kn,n. Journal of Graph Theory, 33 1: 25-31. doi:10.1002/(SICI)1097-0118(200001)33:1<25::AID-JGT3>3.0.CO;2-T
On Alspach's conjecture with two even cycle lengths
Adams, P, Bryant, DE and Khodkar, A (2000) On Alspach's conjecture with two even cycle lengths. Discrete Mathematics, 223 1-3: 1-12. doi:10.1016/S0012-365X(00)00051-0
The fine structure of (v, 3) directed triple systems: v equivalent to 2 (mod 3)
Adams, P, Bryant, DE and Khodkar, A (2000) The fine structure of (v, 3) directed triple systems: v equivalent to 2 (mod 3). Ars Combinatoria, 57 3-11.
The spectrum problem for close m- trails, m 10
Adams, P., Bryant, D. E. and Khodkar, A. (2000) The spectrum problem for close m- trails, m 10. Journal of Combinatorial Mathematics and Combinatorial Computing, 34 223-240.
The spectrum problem for lambda-fold Petersen graph designs
Adams, P., Bryant, D. E. and Khodkar, A. (2000) The spectrum problem for lambda-fold Petersen graph designs. Journal of Combinatorial Mathematics and Combinatorial Computing, 34 159-176.
On the number of repeated triples in balanced ternary designs with index two
Adams, P, Bryant, DE and Khodkar, A (1999) On the number of repeated triples in balanced ternary designs with index two. Utilitas Mathematica, 55 55-64.
Packing and covering the complete graph with cubes
Adams, P., Bryant, D. E. and El-Zanati, S. I. (1999) Packing and covering the complete graph with cubes. Australasian Journal of Combinatorics, 20 267-288.
Small embeddings for partial G-designs when G is bipartite
Bryant, D. E., Khodkar, A. and El-Zanati, S. I. (1999) Small embeddings for partial G-designs when G is bipartite. Bulletin of the Institute of Combinatorics and its Applications, 26 86-90.
Strongly 2-perfect trail systems and related quasigroups
Bryant, D. E. and Oates-Williams, S. (1999) Strongly 2-perfect trail systems and related quasigroups. Australasian Journal of Combinatorics, 20 101-110.
The possible number of cycles in cycle systems
Billington, EJ and Bryant, DE (1999) The possible number of cycles in cycle systems. ARS Combinatoria, 52 65-70.
Generalized optimal lattice covering of finite-dimensional Euclidean space
Bryant, Darryn, Diamond, Phil and Vladimirov, Igor (1998) Generalized optimal lattice covering of finite-dimensional Euclidean space. Linear Algebra and Its Applications, 282 1-3: 311-324.
Bryant, Darryn E. and Maenhaut, Barbara M. (1998) Defining sets of G-designs. The Australasian Journal of Combinatorics, 17 257-266.
On orthogonal double covers of graphs
Bryant, Darryn E. and Khodkar, A. (1998) On orthogonal double covers of graphs. Designs, Codes and Cryptography, 13 2: 103-105. doi:10.1023/A:1008283627078
Bryant, DE, Khodkar, A and Fu, HL (1998) (m,n)-cycle systems. Journal of Statistical Planning And Inference, 74 2: 365-370. doi:10.1016/S0378-3758(98)00084-6
Adams, P, Bryant, DE and Khodkar, A (1998) 3,5-cycle decompositions. Journal of Combinatorial Designs, 6 2: 91-110. doi:10.1002/(SICI)1520-6610(1998)6:2<91::AID-JCD2>3.0.CO;2-Q
5-cycle systems of K-v-F with a hole
Bryant, DE and Khodkar, A (1998) 5-cycle systems of K-v-F with a hole. Utilitas Mathematica, 54 59-73.
Generalized optimal lattice covering of finite-dimensional Euclidean space
Bryant, D, Diamond, P and Vladimirov, I (1998) Generalized optimal lattice covering of finite-dimensional Euclidean space. Linear Algebra And Its Applications, 282 1-3: 311-324. doi:10.1016/S0024-3795(98)10081-2
Bryant, DE (1997) 2m-cycle systems of K2m+1/C-m. Graphs And Combinatorics, 13 3: 227-229.
Embeddings of m-cycle systems and incomplete m-cycle systems: m<=14
Bryant, DE, Rodger, CA and Spicer, ER (1997) Embeddings of m-cycle systems and incomplete m-cycle systems: m<=14. Discrete Mathematics, 171 1-3: 55-75. doi:10.1016/S0012-365X(96)00072-6
Strongly 2-perfect cycle systems and their quasigroups
Bryant, DE and OatesWilliams, S (1997) Strongly 2-perfect cycle systems and their quasigroups. Discrete Mathematics, 167 167-174. doi:10.1016/S0012-365X(96)00225-7
d-cube decompositions of K-n/K-m
Adams, P, Bryant, DE, ElZanati, SI and VandenEynden, C (1997) d-cube decompositions of K-n/K-m. Graphs And Combinatorics, 13 1: 1-7. doi:10.1007/BF01202232
i-perfect m-cycle systems, m ≤ 19
Adams P. and Bryant D.E. (1997) i-perfect m-cycle systems, m ≤ 19. Aequationes Mathematicae, 53 1-2: 275-294. doi:10.1007/BF02215976
The spectrum for lambda-fold Steiner pentagon systems
Adams, P, Billington, EJ and Bryant, DE (1996) The spectrum for lambda-fold Steiner pentagon systems. Journal of Statistical Planning and Inference, 56 1: 3-15.
The spectrum problem for the Petersen graph
Adams, P and Bryant, DE (1996) The spectrum problem for the Petersen graph. Journal of Graph Theory, 22 2: 175-180. doi:10.1002/(SICI)1097-0118(199606)22:2<175::AID-JGT8>3.0.CO;2-K
A special class of nested Steiner triple systems
Bryant, DE (1996) A special class of nested Steiner triple systems. Discrete Mathematics, 152 1-3: 315-320. doi:10.1016/0012-365X(94)00247-G
Partitionable perfect cycle systems with cycle lengths 6 and 8
Adams, Peter, Billington, Elizabeth J. and Bryant, Darryn E. (1996) Partitionable perfect cycle systems with cycle lengths 6 and 8. Discrete Mathematics, 149 1-3: 1-9.
Partitionable perfect cycle systems with cycle lengths 6 and 8
Adams, P, Billington, EJ and Bryant, DE (1996) Partitionable perfect cycle systems with cycle lengths 6 and 8. Discrete Mathematics, 149 1-3: 1-9. doi:10.1016/0012-365X(94)00305-3
2-perfect directed m-cycle systems can be equationally defined for m=3,4, and 5 only
Bryant, DE and Lindner, CC (1996) 2-perfect directed m-cycle systems can be equationally defined for m=3,4, and 5 only. Journal of Statistical Planning And Inference, 56 1: 57-63. doi:10.1016/S0378-3758(96)00009-2
2-perfect m-cycle systems can be equationally defined for m=3, 5, and 7 only
Bryant, DE and Lindner, CC (1996) 2-perfect m-cycle systems can be equationally defined for m=3, 5, and 7 only. Algebra Universalis, 35 1: 1-7. doi:10.1007/BF01190966
Bryant, Darryn E., Hoffman, D. G. and Rodger, C. A. (1996) 5-cycle systems with holes. Designs, Codes, and Cryptography, 8 1-2: 103-108. doi:10.1007/BF00130571
On the existence of super-simple designs with block size 4
Adams P., Bryant D.E. and Khodkar A. (1996) On the existence of super-simple designs with block size 4. Aequationes Mathematicae, 51 3: 230-246.
A Note On Varieties of Groupoids Arising From M-Cycle Systems
Bryant, DE (1995) A Note On Varieties of Groupoids Arising From M-Cycle Systems. Journal of Algebraic Combinatorics, 4 3: 197-200. doi:10.1023/A:1022423910787
Mendelsohn Designs Associated with a Class of Idempotent Quasi-Groups
Bryant, DE and Oateswilliams, S (1995) Mendelsohn Designs Associated with a Class of Idempotent Quasi-Groups. Discrete Mathematics, 138 1-3: 161-167. doi:10.1016/0012-365X(94)00197-Q
Decomposing the Complete Graph Into Cycles of Many Lengths
Bryant, DE and Adams, P (1995) Decomposing the Complete Graph Into Cycles of Many Lengths. Graphs and Combinatorics, 11 2: 97-102. doi:10.1007/BF01929478
Decompositions of Directed-Graphs with Loops and Related Algebras
Bryant, DE (1994) Decompositions of Directed-Graphs with Loops and Related Algebras. Ars Combinatoria, 38 129-136.
The Doyen-Wilson Theorem Extended to 5-Cycles
Bryant, DE and Rodger, CA (1994) The Doyen-Wilson Theorem Extended to 5-Cycles. Journal of Combinatorial Theory Series a, 68 1: 218-225. doi:10.1016/0097-3165(94)90101-5
Constructing Identities for Finite Quasi-Groups
Bryant, DE and Oateswilliams, S (1994) Constructing Identities for Finite Quasi-Groups. Communications in Algebra, 22 5: 1783-1795. doi:10.1080/00927879408824935
Varieties of Quasi-Groups and Related Topics
Bryant, DE (1993) Varieties of Quasi-Groups and Related Topics. Bulletin of the Australian Mathematical Society, 48 1: 171-172.
Inferring an original sequence from erroneous copies: A Bayesian approach
Keith, J. M., Adams, P., Bryant, D. E., Mitchelson, K. R., Cochran, D.A.E. and Lala, G. H. (2003). Inferring an original sequence from erroneous copies: A Bayesian approach. In: Y-P. Phoebe Chen, Conferences in Research and Practice in Information Technology. First Asia-Pacific Bioinformatics Conference, Adelaide Conference Centre, (23-28). 3-6 February, 2003.
Colloidal barcoding in combinatorial chemistry
Battersby, B. J., Bryant, D. E., Meutermans, W. and Smythe, M. L. (2001). Colloidal barcoding in combinatorial chemistry. In: Innovation and Perspectives in Solid Phase Synthesis and Combinatorial Libraries. Innovation & Perspectives in Solid Phase Synthesis & Combinatl, York, England, (199-202). 31 Aug - 4 Sept, 1999.
Matchings in Combinatorial Structures (ARC Discovery Project administered by Monash University)
(2015–2019) Monash University
Decompositions of graphs into cycles
(2015–2018) Vice-Chancellor's Senior Research Fellowship
The Oberwolfach Problem and related Graph Factorisations
(2015–2018) ARC Discovery Projects
A new approach to compressed sensing
(2012–2016) ARC Discovery Projects
Decompositions of graphs into cycles: Alspach's Conjecture and the Oberwolfach Problem.
(2012–2015) ARC Discovery Projects
Cycle decompositions of graphs
(2007–2011) ARC Discovery Projects
Analysis of the Structure of Latin Squares (ARC Discovery project administered by Monash University)
(2006–2010) Monash University
Mutagenesis and combinatorial algorithms for sequencing problematic genomic regions.
(2002–2006) ARC Discovery Projects
Emerging applications of advanced computational methods and discrete mathematics.
(2002–2003) ARC Discovery Projects
Combinatorial graph decomposition techniques and DNA sequencing by hybridisation
(1999) UQ Foundation Research Excellence Awards - DVC(R) Funding
Rapid DNA sequencing by hybridization of a patterned colloidal array
(1998–2000) ARC Australian Research Council (Large grants)
Embedding Cycle Systems of Multigraphs
(1998) University of Queensland New Staff Research Grant
Statistical laws for computational collapse of chaotic systems
(1997–1999) ARC Australian Research Council (Large grants)
(1997–1999) ARC Australian Research Council (Large grants)
Large sets of cycle systems and related designs
(1996–1998) ARC Australian Postdoctoral Research Fellowship
Parallel algorithms and computational techniques in combinatorial design theory
(1995–1997) ARC Australian Research Council (Large grants)
Path decomposition of graphs
Doctor Philosophy — Principal Advisor
Factorisations of graphs.
Master Philosophy — Associate Advisor
Other advisors:
(2014) Doctor Philosophy — Principal Advisor
Other advisors:
Some results on decompositions of circulant graphs and embeddings of partial cycle systems
(2011) Doctor Philosophy — Principal Advisor
Other advisors:
EMBEDDING, EXISTENCE AND COMPLETION PROBLEMS FOR LATIN SQUARES
() Doctor Philosophy — Principal Advisor
Other advisors:
Some results on Steiner Triple Systems and Cycle Decompositions
(2008) Doctor Philosophy — Principal Advisor
Other advisors:
Topics in Graph Decomposition and Related Algebras
(2008) Doctor Philosophy — Principal Advisor
Other advisors:
ON HAMILTON CYCLES AND HAMILTON CYCLE DECOMPOSITIONS OF GRAPHS BASED ON GROUPS
(2006) Doctor Philosophy — Principal Advisor
Other advisors:
Perfect 1-Factorisations of Circulant Graphs
(2014) Doctor Philosophy — Associate Advisor
Other advisors:
Coloured graph decompositions
(2005) Doctor Philosophy — Associate Advisor
Other advisors:
PARTIAL GRAPH DESIGN EMBEDDINGS AND RELATED PROBLEMS
(2005) Doctor Philosophy — Associate Advisor
Other advisors:
Note for students: The possible research projects listed on this page may not be comprehensive or up to date. Always feel free to contact the staff for more information, and also with your own research ideas.
Hamilton cycle decompositions of Cayley graphs and related topics
There is an unsolved conjecture that every connected 2k-regular Cayley graph on a finite abelian group has a decomposition into k Hamilton cycles. Cayley graphs are graphs based on groups and students who like group theory or graph theory will enjoy working on this and related problems.
The 2-factorisation problem for complete graphs
This project examines the existence of 2-factorisations of complete graphs in which the 2-factors are isomorphic to given 2-regular graphs. Using computers the problem has been completely solved for complete graphs of order less than 20 and several infinite families of results are known. However much work remains to be done on this problem and there is plenty of scope for new discoveries to be made by students who enjoy design theory or graph theory.