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)

141 - 159 of 159 works

1997

Journal Article

Embeddings of m-cycle systems and incomplete m-cycle systems: m<=14

Bryant, DE, Rodger, CA and Spicer, ER (1997). Embeddings of m-cycle systems and incomplete m-cycle systems: m<=14. Discrete Mathematics, 171 (1-3), 55-75. doi: 10.1016/S0012-365X(96)00072-6

Embeddings of m-cycle systems and incomplete m-cycle systems: m<=14

1996

Journal Article

The spectrum for lambda-fold Steiner pentagon systems

Adams, P, Billington, EJ and Bryant, DE (1996). The spectrum for lambda-fold Steiner pentagon systems. Journal of Statistical Planning and Inference, 56 (1), 3-15.

The spectrum for lambda-fold Steiner pentagon systems

1996

Journal Article

The spectrum problem for the Petersen graph

Adams, P and Bryant, DE (1996). The spectrum problem for the Petersen graph. Journal of Graph Theory, 22 (2), 175-180. doi: 10.1002/(SICI)1097-0118(199606)22:23.0.CO;2-K

The spectrum problem for the Petersen graph

1996

Journal Article

A special class of nested Steiner triple systems

Bryant, DE (1996). A special class of nested Steiner triple systems. Discrete Mathematics, 152 (1-3), 315-320. doi: 10.1016/0012-365X(94)00247-G

A special class of nested Steiner triple systems

1996

Journal Article

Partitionable perfect cycle systems with cycle lengths 6 and 8

Adams, Peter, Billington, Elizabeth J. and Bryant, Darryn E. (1996). Partitionable perfect cycle systems with cycle lengths 6 and 8. Discrete Mathematics, 149 (1-3), 1-9.

Partitionable perfect cycle systems with cycle lengths 6 and 8

1996

Journal Article

Partitionable perfect cycle systems with cycle lengths 6 and 8

Adams, P, Billington, EJ and Bryant, DE (1996). Partitionable perfect cycle systems with cycle lengths 6 and 8. Discrete Mathematics, 149 (1-3), 1-9. doi: 10.1016/0012-365X(94)00305-3

Partitionable perfect cycle systems with cycle lengths 6 and 8

1996

Journal Article

5-cycle systems with holes

Bryant, Darryn E., Hoffman, D. G. and Rodger, C. A. (1996). 5-cycle systems with holes. Designs, Codes, and Cryptography, 8 (1-2), 103-108. doi: 10.1007/BF00130571

5-cycle systems with holes

1996

Journal Article

2-perfect directed m-cycle systems can be equationally defined for m=3,4, and 5 only

Bryant, DE and Lindner, CC (1996). 2-perfect directed m-cycle systems can be equationally defined for m=3,4, and 5 only. Journal of Statistical Planning And Inference, 56 (1), 57-63. doi: 10.1016/S0378-3758(96)00009-2

2-perfect directed m-cycle systems can be equationally defined for m=3,4, and 5 only

1996

Journal Article

On the existence of super-simple designs with block size 4

Adams P., Bryant D.E. and Khodkar A. (1996). On the existence of super-simple designs with block size 4. Aequationes Mathematicae, 51 (3), 230-246. doi: 10.1007/BF01833280

On the existence of super-simple designs with block size 4

1996

Journal Article

2-perfect m-cycle systems can be equationally defined for m=3, 5, and 7 only

Bryant, DE and Lindner, CC (1996). 2-perfect m-cycle systems can be equationally defined for m=3, 5, and 7 only. Algebra Universalis, 35 (1), 1-7. doi: 10.1007/BF01190966

2-perfect m-cycle systems can be equationally defined for m=3, 5, and 7 only

1995

Journal Article

A Note On Varieties of Groupoids Arising From M-Cycle Systems

Bryant, DE (1995). A Note On Varieties of Groupoids Arising From M-Cycle Systems. Journal of Algebraic Combinatorics, 4 (3), 197-200. doi: 10.1023/A:1022423910787

A Note On Varieties of Groupoids Arising From M-Cycle Systems

1995

Journal Article

Mendelsohn Designs Associated with a Class of Idempotent Quasi-Groups

Bryant, DE and Oateswilliams, S (1995). Mendelsohn Designs Associated with a Class of Idempotent Quasi-Groups. Discrete Mathematics, 138 (1-3), 161-167. doi: 10.1016/0012-365X(94)00197-Q

Mendelsohn Designs Associated with a Class of Idempotent Quasi-Groups

1995

Journal Article

Decomposing the Complete Graph Into Cycles of Many Lengths

Bryant, DE and Adams, P (1995). Decomposing the Complete Graph Into Cycles of Many Lengths. Graphs and Combinatorics, 11 (2), 97-102. doi: 10.1007/BF01929478

Decomposing the Complete Graph Into Cycles of Many Lengths

1994

Journal Article

Decompositions of Directed-Graphs with Loops and Related Algebras

Bryant, DE (1994). Decompositions of Directed-Graphs with Loops and Related Algebras. Ars Combinatoria, 38, 129-136.

Decompositions of Directed-Graphs with Loops and Related Algebras

1994

Journal Article

The Doyen-Wilson Theorem Extended to 5-Cycles

Bryant, DE and Rodger, CA (1994). The Doyen-Wilson Theorem Extended to 5-Cycles. Journal of Combinatorial Theory Series a, 68 (1), 218-225. doi: 10.1016/0097-3165(94)90101-5

The Doyen-Wilson Theorem Extended to 5-Cycles

1994

Journal Article

Constructing Identities for Finite Quasi-Groups

Bryant, DE and Oateswilliams, S (1994). Constructing Identities for Finite Quasi-Groups. Communications in Algebra, 22 (5), 1783-1795. doi: 10.1080/00927879408824935

Constructing Identities for Finite Quasi-Groups

1994

Journal Article

On the doyen‐wilson theorem for m‐cycle systems

Bryant, Darryn E. and Rodger, C. A. (1994). On the doyen‐wilson theorem for m‐cycle systems. Journal of Combinatorial Designs, 2 (4), 253-271. doi: 10.1002/jcd.3180020405

On the doyen‐wilson theorem for m‐cycle systems

1993

Journal Article

Varieties of Quasi-Groups and Related Topics

Bryant, DE (1993). Varieties of Quasi-Groups and Related Topics. Bulletin of the Australian Mathematical Society, 48 (1), 171-172. doi: 10.1017/S0004972700015574

Varieties of Quasi-Groups and Related Topics

1992

Journal Article

Varieties of quasigroups arising from 2-perfect m-cycle systems

Bryant, D. E. (1992). Varieties of quasigroups arising from 2-perfect m-cycle systems. Designs, Codes and Cryptography, 2 (2), 159-168. doi: 10.1007/BF00124894

Varieties of quasigroups arising from 2-perfect m-cycle systems

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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