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)

121 - 140 of 159 works

2000

Journal Article

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)33:13.0.CO;2-T

Maximal sets of Hamilton cycles in Kn,n

1999

Journal Article

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.

Packing and covering the complete graph with cubes

1999

Journal Article

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.

Small embeddings for partial G-designs when G is bipartite

1999

Journal Article

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.

On the number of repeated triples in balanced ternary designs with index two

1999

Journal Article

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.

The possible number of cycles in cycle systems

1999

Journal Article

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.

Strongly 2-perfect trail systems and related quasigroups

1998

Journal Article

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.

Generalized optimal lattice covering of finite-dimensional Euclidean space

1998

Journal Article

Defining sets of G-designs

Bryant, Darryn E. and Maenhaut, Barbara M. (1998). Defining sets of G-designs. The Australasian Journal of Combinatorics, 17, 257-266.

Defining sets of G-designs

1998

Journal Article

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

On orthogonal double covers of graphs

1998

Journal Article

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

Generalized optimal lattice covering of finite-dimensional Euclidean space

1998

Journal Article

3,5-cycle decompositions

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)6:23.0.CO;2-Q

3,5-cycle decompositions

1998

Journal Article

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.

5-cycle systems of K-v-F with a hole

1998

Journal Article

(m,n)-cycle systems

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

(m,n)-cycle systems

1997

Journal Article

Factorizations of complete multigraphs

Battersby, B. J., Bryant, D. E. and Rodger, C. A. (1997). Factorizations of complete multigraphs. Australasian Journal of Combinatorics, 16, 35-43.

Factorizations of complete multigraphs

1997

Journal Article

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

i-perfect m-cycle systems, m ≤ 19

1997

Journal Article

2m-cycle systems of K2m+1/C-m

Bryant, DE (1997). 2m-cycle systems of K2m+1/C-m. Graphs And Combinatorics, 13 (3), 227-229. doi: 10.1007/BF03352999

2m-cycle systems of K2m+1/C-m

1997

Journal Article

On the volume of trades in triple systems

Bryant, D. E. (1997). On the volume of trades in triple systems. Australasian Journal of Combinatorics, 15, 161-176.

On the volume of trades in triple systems

1997

Journal Article

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

d-cube decompositions of K-n/K-m

1997

Journal Article

2m-Cycle systems of K2m+1\Cm

Bryant, D. E. (1997). 2m-Cycle systems of K2m+1\Cm. Graphs and Combinatorics, 13 (3), 227-229.

2m-Cycle systems of K2m+1\Cm

1997

Journal Article

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

Strongly 2-perfect cycle systems and their quasigroups

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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