A/Prof Daniel Horsley

Research Overview

My research mostly concerns combinatorial designs and edge decompositions of graphs. Often one of the most useful ways to view a combinatorial design is as an edge-decomposition of an appropriate graph or hypergraph: a (v,k,1) block design, for example, is an edge decomposition of a complete graph of order v into complete graphs of order k. I often study completion and embedding of block designs, matchings in block designs, and colourings of block designs. Relatedly, I am interested in bounds on packing and covering numbers. I have also considered questions concerning to edge decompositions of graphs into cycles and 2-factors. Finally, I also do work on combinatorial arrays with applications in designing testing schemes and in sampling signals.

Selected Publications

[1] Cameron, Rosalind A. ; Horsley, Daniel. "Decompositions of complete multigraphs into stars of varying sizes". In: Journal of Combinatorial Theory, Series B. 2020 ; Vol. 145. pp. 32-64. https://doi.org/10.1016/j.jctb.2020.05.001

[2] Horsley, Daniel. "Generalising Fisher’s inequality to coverings and packings". In: Combinatorica. 2017 ; Vol. 37, No. 4. pp. 673-696. https://doi.org/10.1007/s00493-016-3326-9

[3] Bryant, Darryn Edward ; Horsley, Daniel. "Steiner triple systems without parallel classes". In: SIAM Journal on Discrete Mathematics. 2015 ; Vol. 29, No. 1. pp. 693-696. https://doi.org/10.1137/140996999

[4] Bryant, Darryn ; Horsley, Daniel ; Pettersson, William. "Cycle decompositions V: complete graphs into cycles of arbitrary lengths". In: Proceedings of the London Mathematical Society. 2014 ; Vol. 108, No. 5. pp. 1153 - 1192. https://doi.org/10.1112/plms/pdt051

[5] Chee, Yeow Meng ; Colbourn, Charles J ; Horsley, Daniel ; Zhou, Junling. "Sequence covering arrays". In: SIAM Journal on Discrete Mathematics. 2013 ; Vol. 27, No. 4. pp. 1844 - 1861. https://doi.org/10.1137/120894099