Overview
Background
Dr Sara Davies (née Herke) received her PhD in mathematics in 2014. She has also published under the names Sarada Herke and Sara Herke.
Availability
- Dr Sara Davies is:
- Available for supervision
Qualifications
- Doctor of Philosophy, The University of Queensland
Research interests
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Graph theory and design theory
My research has been focused in graph theory and related areas of combinatorics such as design theory, hypergraphs and latin squares. Understanding the properties of graphs and hypergraphs is important for modelling a variety of relational systems; applications range from transportation networks, biological models and efficient storage of data. Design theory and latin squares also have vast applications, including the design of experiments and error-correcting codes. Some major themes of my research are graph decompositions, factorisations of graphs, and optimally covering the edges of hypergraphs.
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Scholarship of teaching and learning
Active and blended learning; Perceptions of STEM topic among science students; Authentic assessment; Criteria-based grading
Works
Search Professor Sara Davies’s works on UQ eSpace
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
Featured
2018
Journal Article
Parity of sets of mutually orthogonal Latin squares
Francetic, Nevena, Herke, Sarada and Wanless, Ian M. (2018). Parity of sets of mutually orthogonal Latin squares. Journal of Combinatorial Theory Series A, 155, 67-99. doi: 10.1016/j.jcta.2017.10.006
Featured
2017
Journal Article
On Ryser's conjecture for linear intersecting multipartite hypergraphs
Francetic, Nevena, Herke, Sarada, McKay, Brendan D. and Wanless, Ian M. (2017). On Ryser's conjecture for linear intersecting multipartite hypergraphs. European Journal of Combinatorics, 61, 91-105. doi: 10.1016/j.ejc.2016.10.004
Featured
2015
Journal Article
More nonexistence results for symmetric pair coverings
Francetic, Nevena, Herke, Sarada and Horsley, Daniel (2015). More nonexistence results for symmetric pair coverings. Linear Algebra and Its Applications, 487 13357, 43-73. doi: 10.1016/j.laa.2015.09.006
Featured
2009
Journal Article
Radial trees
Herke, S. and Mynhardt, C. M. (2009). Radial trees. Discrete Mathematics, 309 (20), 5950-5962. doi: 10.1016/j.disc.2009.04.024
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.
2023
Journal Article
Perfect 1-factorisations of complete k-uniform hypergraphs
Davies, Sara, Maenhaut, Barbara and Mitchell, Jeremy (2023). Perfect 1-factorisations of complete k-uniform hypergraphs. Australasian Journal of Combinatorics, 85 (1), 35-48.
2023
Journal Article
What Are the Chances? Exploring Conditional Probability in Context
Greenwood, Ava, Davies, Sara and McIntyre, Timothy J. (2023). What Are the Chances? Exploring Conditional Probability in Context. Australian Mathematics Education Journal, 5 (3), 26-32.
2019
Journal Article
MAX for k-independence in multigraphs
Francetić, Nevena, Herke, Sara and Horsley, Daniel (2019). MAX for k-independence in multigraphs. Discrete Applied Mathematics, 265, 56-68. doi: 10.1016/j.dam.2019.03.007
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
2019
Conference Publication
The effect of an interdisciplinary science course on student perceptions of computer programming
Piggott, Adam, Herke, Sara, McIntyre, Timothy and Bulmer, Michael (2019). The effect of an interdisciplinary science course on student perceptions of computer programming. Australian Conference on Science and Mathematics Education 2019, Sydney, Australia, 2-4 October 2019. Open Journal Systems.
2014
Journal Article
Perfect 1-factorizations of a family of Cayley graphs
Herke, Sarada and Maenhaut, Barbara (2014). Perfect 1-factorizations of a family of Cayley graphs. Journal of Combinatorial Designs, 23 (9), 369-399. doi: 10.1002/jcd.21399
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.
2014
Journal Article
On the perfect 1-factorisation problem for circulant graphs of degree 4
Herke, Sarada (2014). On the perfect 1-factorisation problem for circulant graphs of degree 4. Australasian Journal of Combinatorics, 60, 79-108.
2013
Other Outputs
Perfect 1-Factorisations of Circulant Graphs
Herke, Sarada Rachelle Anne (2013). Perfect 1-Factorisations of Circulant Graphs. PhD Thesis, School of Mathematics and Physics, The University of Queensland. doi: 10.14264/uql.2014.98
2013
Journal Article
Perfect 1-factorisations of circulants with small degree
Herke, Sarada and Maenhaut, Barbara (2013). Perfect 1-factorisations of circulants with small degree. Electronic Journal of Combinatorics, 20 (1). doi: 10.37236/2264
2011
Journal Article
Broadcasts and domination in trees
Cockayne, E.J., Herke, S. and Mynhardt, C.M. (2011). Broadcasts and domination in trees. Discrete Mathematics, 311 (13), 1235-1246. doi: 10.1016/j.disc.2009.12.012
2010
Journal Article
On the possible orders of a basis for a finite cyclic group
Dukes, Peter, Hegarty, Peter and Herke, Sarada (2010). On the possible orders of a basis for a finite cyclic group. Electronic Journal of Combinatorics, 17 (1), 1-10. doi: 10.37236/351
Supervision
Availability
- Dr Sara Davies is:
- Available for supervision
Before you email them, read our advice on how to contact a supervisor.
Supervision history
Current supervision
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Doctor Philosophy
Hypergraphs with high chromatic index
Principal Advisor
Other advisors: Professor Darryn Bryant
Completed supervision
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2024
Doctor Philosophy
Generalisations of Uniform and Perfect 1-Factorisations of Graphs
Associate Advisor
Other advisors: Associate Professor Barbara Maenhaut
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2024
Doctor Philosophy
Hamilton decompositions and edge colourings of graph compositions
Associate Advisor
Other advisors: Professor Darryn Bryant
Media
Enquiries
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