Professor

Darryn Bryant

Email: 
Phone: 
+61 7 336 51342

Background

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.

Availability

Professor Darryn Bryant is:
Available for supervision
Media expert

Fields of research

Pure mathematics

Qualifications

  • Bachelor of Science, The University of Queensland
  • Masters (Coursework), The University of Queensland
  • Doctor of Philosophy, The University of Queensland

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.

Search Professor Darryn Bryant’s works on UQ eSpace

159 works between 1992 and 2024
All (159) Journal Article (152) Book Chapter (4) Conference Publication (3)

41 - 60 of 159 works

2009

Journal Article

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

Perpendicular Rectangular Latin Arrays

2009

Journal Article

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

The spectrum for quasigroups with cyclic automorphisms and additional symmetries

2009

Journal Article

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.

Some results on decompositions of low degree circulant graphs

2009

Journal Article

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

A proof of Lindner's conjecture on embeddings of partial steiner triple systems

2008

Journal Article

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) R56, Article Number: R56. doi: 10.37236/780

Completing partial Latin squares with two filled rows and two filled columns

2008

Journal Article

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

Almost regular edge colorings and regular decompositions of complete graphs

2008

Journal Article

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

A survey on the existence of G-designs

2008

Journal Article

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

Packing cycles in complete graphs

2007

Book Chapter

Graph Decompositions

Bryant, D. E. and El-Zanati, S. (2007). Graph Decompositions. Handbook of Combinatorial Designs. (pp. 477-486) edited by Colbourn, C. J. and Dinitz, J. H.. New York: Chapman & Hall/CRC.

Graph Decompositions

2007

Journal Article

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.

Cycle decompositions of complete graphs

2007

Journal Article

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.

Some equitably 2-colourable cycle decompositions

2007

Book Chapter

Sequencing aided by mutagenesis facilitates the de novo sequencing of megabase DNA fragments by short read lengths

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. New High Throughput Technologies for DNA Sequencing and Genomics. (pp. 303-326) edited by Mitchelson, K. R.. Netherlands: Elsevier. doi: 10.1016/S1871-0069(06)02010-6

Sequencing aided by mutagenesis facilitates the de novo sequencing of megabase DNA fragments by short read lengths

2007

Book Chapter

Cycle decompositions

Bryant, D. E. and Rodger, C. (2007). Cycle decompositions. Handbook of Combinatorial Designs. (pp. 373-382) edited by Colbourn, C. J. and Dinitz, J. H.. New York: Chapman & Hall/CRC.

Cycle decompositions

2007

Journal Article

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

Star factorizations of graph products (vol 36, pg 59, 2001)

2007

Journal Article

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

Embedding partial totally symmetric quasigroups

2006

Journal Article

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

Edge-coloured cube decompositions

2006

Journal Article

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.

The Embedding Problem for Partial Steiner Triple Systems

2006

Journal Article

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

New families of atomic Latin squares and perfect 1-factorisations

2006

Journal Article

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.

Diagonally switchable 4-cycle systems

2006

Journal Article

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

Steiner triple systems with two disjoint subsystems

Current funding

  • 2024 - 2028
    Fractional decomposition of graphs and the Nash-Williams conjecture (ARC Discovery Project externally administered by Monash University)
    Monash University
    Open grant

Past funding

  • 2015 - 2018
    Decompositions of graphs into cycles
    Vice-Chancellor's Senior Research Fellowship
    Open grant
  • 2015 - 2019
    Matchings in Combinatorial Structures (ARC Discovery Project administered by Monash University)
    Monash University
    Open grant
  • 2015 - 2018
    The Oberwolfach Problem and related Graph Factorisations
    ARC Discovery Projects
    Open grant
  • 2012 - 2016
    A new approach to compressed sensing
    ARC Discovery Projects
    Open grant
  • 2012 - 2015
    Decompositions of graphs into cycles: Alspach's Conjecture and the Oberwolfach Problem.
    ARC Discovery Projects
    Open grant
  • 2012
    ResTeach Funding 2012 0.2 FTE School of Math & Physics
    UQ ResTeach
    Open grant
  • 2007 - 2011
    Cycle decompositions of graphs
    ARC Discovery Projects
    Open grant
  • 2006 - 2010
    Analysis of the Structure of Latin Squares (ARC Discovery project administered by Monash University)
    Monash University
    Open grant
  • 2003
    To Expand Research On The Isolation And Direct To Work On New Combinatorial Graph Decompositions Techniques
    UQ Travel Grants Scheme
    Open grant
  • 2002 - 2003
    Emerging applications of advanced computational methods and discrete mathematics.
    ARC Discovery Projects
    Open grant
  • 2002 - 2006
    Mutagenesis and combinatorial algorithms for sequencing problematic genomic regions.
    ARC Discovery Projects
    Open grant
  • 1999
    Combinatorial graph decomposition techniques and DNA sequencing by hybridisation
    UQ Foundation Research Excellence Awards - DVC(R) Funding
    Open grant
  • 1998
    Embedding Cycle Systems of Multigraphs
    University of Queensland New Staff Research Grant
    Open grant
  • 1998 - 2000
    Rapid DNA sequencing by hybridization of a patterned colloidal array
    ARC Australian Research Council (Large grants)
    Open grant
  • 1997 - 1999
    Statistical laws for computational collapse of chaotic systems
    ARC Australian Research Council (Large grants)
    Open grant
  • 1997 - 1999
    Trades in graphs
    ARC Australian Research Council (Large grants)
    Open grant
  • 1996 - 1998
    Large sets of cycle systems and related designs
    ARC Australian Postdoctoral Research Fellowship
    Open grant
  • 1995 - 1997
    Parallel algorithms and computational techniques in combinatorial design theory
    ARC Australian Research Council (Large grants)
    Open grant

Availability

Professor Darryn Bryant is:
Available for supervision

Before you email them, read our advice on how to contact a supervisor.

Available projects

  • 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.

  • 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.

Supervision history

Current supervision

  • Doctor Philosophy

    Analytic number theory and applications to graph theory

    Associate Advisor

    Other advisors: Dr Adrian Dudek

  • Doctor Philosophy

    Hypergraphs with high chromatic index

    Associate Advisor

    Other advisors: Dr Sara Davies

Completed supervision

Enquiries

Contact Professor Darryn Bryant directly for media enquiries about:

  • Combinatorics
  • Design theory - mathematics
  • Graph theory - mathematics
  • Maths - combinatorics

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