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Professor

Darryn Bryant

Email: 
Phone: 
+61 7 336 51342

Overview

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

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.

Works

Search Professor Darryn Bryant’s works on UQ eSpace

159 works between 1992 and 2024

1 - 20 of 159 works

2024

Journal Article

Almost resolvable duplicated Steiner triple systems

Bryant, Darryn, Davies, Sara and Neubecker, Jack (2024). Almost resolvable duplicated Steiner triple systems. Australasian Journal of Combinatorics, 88 (2), 256-265.

Almost resolvable duplicated Steiner triple systems

2021

Journal Article

On the Steiner Quadruple System with Ten Points

Brier, Robert and Bryant, Darryn (2021). On the Steiner Quadruple System with Ten Points. Bulletin of the Institute of Combinatorics and its Applications, 91, 115-127.

On the Steiner Quadruple System with Ten Points

2020

Journal Article

On determining when small embeddings of partial Steiner triple systems exist

Bryant, Darryn, De Vas Gunasekara, Ajani and Horsley, Daniel (2020). On determining when small embeddings of partial Steiner triple systems exist. Journal of Combinatorial Designs, 28 (8) jcd.21715, 568-579. doi: 10.1002/jcd.21715

On determining when small embeddings of partial Steiner triple systems exist

2019

Journal Article

Hamilton path decompositions of complete multipartite graphs

Bryant, Darryn, Hang, Hao Chuien and Herke, Sarada (2019). Hamilton path decompositions of complete multipartite graphs. Journal of Combinatorial Theory. Series B, 135, 1-15. doi: 10.1016/j.jctb.2018.07.006

Hamilton path decompositions of complete multipartite graphs

2018

Journal Article

Uniform decompositions of complete multigraphs into cycles

Berry, Duncan, Bryant, Darryn, Dean, Matthew and Maenhaut, Barbara (2018). Uniform decompositions of complete multigraphs into cycles. Journal of Combinatorial Designs, 26 (12), 595-615. doi: 10.1002/jcd.21630

Uniform decompositions of complete multigraphs into cycles

2018

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

On Hamilton decompositions of infinite circulant graphs

2018

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

Decompositions of complete multigraphs into cycles of varying lengths

2018

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.

On Hamilton decompositions of line graphs of non-hamiltonian graphs and graphs without separating transitions

2017

Journal Article

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

Steiner triple systems with high chromatic index

2017

Journal Article

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) 7954982, 4850-4859. doi: 10.1109/TIT.2017.2717584

Compressed sensing with combinatorial designs: theory and simulations

2016

Journal Article

On almost-regular edge colourings of hypergraphs

Bryant, Darryn (2016). On almost-regular edge colourings of hypergraphs. Electronic Journal of Combinatorics, 23 (4) #P4.7. doi: 10.37236/5826

On almost-regular edge colourings of hypergraphs

2016

Journal Article

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) P2.1. doi: 10.37236/4634

Decompositions of complete graphs into bipartite 2-regular subgraphs

2016

Journal Article

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. doi: 10.26493/1855-3974.770.150

On factorisations of complete graphs into circulant graphs and the Oberwolfach problem

2015

Journal Article

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

Vertex-transitive graphs that have no Hamilton decomposition

2015

Journal Article

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

An asymptotic existence result on compressed sensing matrices

2015

Journal Article

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

Bipartite 2-factorizations of complete multipartite graphs

2015

Journal Article

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

Steiner Triple Systems Without Parallel Classes

2014

Journal Article

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

Decomposing graphs of high minimum degree into 4-cycles

2014

Journal Article

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

Brushing without capacity restrictions

2014

Journal Article

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

Cycle decompositions V: complete graphs into cycles of arbitrary lengths

Funding

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

Supervision

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

Media

Enquiries

Contact Professor Darryn Bryant directly for media enquiries about:

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

Need help?

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communications@uq.edu.au