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)

21 - 40 of 159 works

2014

Journal Article

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

Vertex-transitive graphs of prime-squared order are Hamilton-decomposable

2014

Journal Article

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.

Decompositions of complete 3-uniform hypergraphs into small 3-uniform hypergraphs

2013

Journal Article

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

A second infinite family of Steiner triple systems without almost parallel classes

2013

Journal Article

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

On the Hamilton-Waterloo problem for bipartite 2-factors

2012

Journal Article

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

Decomposing the complete graph into dodecahedra

2012

Journal Article

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

Small embeddings for partial triple systems of odd index

2012

Journal Article

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

Paley graphs have Hamilton decompositions

2012

Journal Article

Nonextendible Latin Cuboids

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

Nonextendible Latin Cuboids

2011

Journal Article

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 the non-existence of pair covering designs with at least as many points as blocks

2011

Journal Article

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 bipartite 2-factorizations of K(n)-I and the Oberwolfach problem

2011

Journal Article

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.

On the existence and embedding of edge-coloured graph decompositions

2011

Journal Article

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

Cycle Decompositions of Complete Multigraphs

2010

Journal Article

Defining scaffold geometries for interacting with proteins: Geometrical classification of secondary structure linking regions

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

Defining scaffold geometries for interacting with proteins: Geometrical classification of secondary structure linking regions

2010

Journal Article

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

An asymptotic solution to the cycle decomposition problem for complete graphs

2010

Journal Article

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

Decompositions of complete graphs into long cycles

2010

Journal Article

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

Packing paths in complete graphs

2009

Journal Article

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

Complete solutions to the Oberwolfach problem for an infinite set of orders

2009

Journal Article

Completing partial commutative quasigroups constructed from partial Steiner triple systems is NP-complete

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

Completing partial commutative quasigroups constructed from partial Steiner triple systems is NP-complete

2009

Journal Article

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

Indivisible plexes in latin squares

2009

Journal Article

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

The nonexistence of a (K6-e)-decomposition of the complete graph K29

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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