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
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.
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.
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
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
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
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
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
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.
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
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
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
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
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
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
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
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
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
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
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
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
Funding
Current funding
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.
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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
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2024
Doctor Philosophy
Hamilton decompositions and edge colourings of graph compositions
Principal Advisor
Other advisors: Dr Sara Davies
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2014
Doctor Philosophy
Computational Graph Theory
Principal Advisor
Other advisors: Associate Professor Barbara Maenhaut, Professor Benjamin Burton
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2011
Doctor Philosophy
Some results on decompositions of circulant graphs and embeddings of partial cycle systems
Principal Advisor
Other advisors: Associate Professor Barbara Maenhaut
-
2008
Doctor Philosophy
Topics in Graph Decomposition and Related Algebras
Principal Advisor
Other advisors: Associate Professor Barbara Maenhaut
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2008
Doctor Philosophy
Some results on Steiner Triple Systems and Cycle Decompositions
Principal Advisor
Other advisors: Associate Professor Barbara Maenhaut
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2006
Doctor Philosophy
ON HAMILTON CYCLES AND HAMILTON CYCLE DECOMPOSITIONS OF GRAPHS BASED ON GROUPS
Principal Advisor
-
Doctor Philosophy
EMBEDDING, EXISTENCE AND COMPLETION PROBLEMS FOR LATIN SQUARES
Principal Advisor
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2018
Master Philosophy
Uniform cycle decompositions of complete multigraphs
Associate Advisor
Other advisors: Associate Professor Barbara Maenhaut
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2014
Doctor Philosophy
Perfect 1-Factorisations of Circulant Graphs
Associate Advisor
Other advisors: Associate Professor Barbara Maenhaut
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2005
Doctor Philosophy
PARTIAL GRAPH DESIGN EMBEDDINGS AND RELATED PROBLEMS
Associate Advisor
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2005
Doctor Philosophy
Coloured graph decompositions
Associate Advisor
Media
Enquiries
Contact Professor Darryn Bryant directly for media enquiries about:
- Combinatorics
- Design theory - mathematics
- Graph theory - mathematics
- Maths - combinatorics
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