Professor Darryn Bryant

VC Senior Research Fellow

Mathematics
Faculty of Science
db@maths.uq.edu.au
+61 7 336 51342

Overview

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.

Research Interests

  • Graph theory and design theory
    Various graph decomposition problems including decompositions into Hamilton cycles, embedding problems and perfect factorisations are being investigated. This includes collaborative work with colleagues at The University of Queensland, and in the UK, USA and Canada.

Qualifications

  • PhD, The University of Queensland
  • MScSt, The University of Queensland
  • BSc, The University of Queensland

Publications

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Grants

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Supervision

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Available Projects

  • 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.

  • 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.

View all Available Projects

Publications

Book Chapter

  • 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

  • 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.

Journal Article

Conference Publication

  • 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.

  • 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.

Grants (Administered at UQ)

PhD and MPhil Supervision

Current Supervision

  • Doctor Philosophy — Principal Advisor

  • Doctor Philosophy — Associate Advisor

    Other advisors:

Completed Supervision

Possible Research Projects

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.

  • 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.

  • 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.