David A. Pike

activity

20182022

collaborators

5 papers

math.CO2022

Mutually orthogonal cycle systems

Andrea C. Burgess, Nicholas J. Cavenagh, David A. Pike

An $ℓ$ -cycle system $F$ of a graph $Γ$ is a set of $ℓ$ -cycles which partition the edge set of $Γ$ . Two such cycle systems $F$ and $F^{'}$ ar…

math.CO2019

Colourings of star systems

Iren Darijani, David Pike

An $e$ -star is a complete bipartite graph $K_{1, e}$ . An $e$ -star system of order $n > 1$ , $S_{e} (n)$ , is a partition of the edges of the complete graph $K_{n}$ into $e$ -stars. An $e$ -sta…

math.CO2019

The Firebreak Problem

Kathleen D. Barnetson, Andrea C. Burgess, Jessica Enright +3

Suppose we have a network that is represented by a graph $G$ . Potentially a fire (or other type of contagion) might erupt at some vertex of $G$ . We are able to respond to this outb…

math.CO2018

A Perfect One-Factorisation of $K_{56}$

David A. Pike

In 1963, Anton Kotzig conjectured that for each $n \geq 2$ the complete graph $K_{2 n}$ has a perfect one-factorisation (i.e., a decomposition into perfect matchings such that each…

math.CO2018

Decomposable twofold triple systems with non-Hamiltonian 2-block intersection graphs

Rosalind A. Cameron, David A. Pike

The 2-block intersection graph (2-BIG) of a twofold triple system (TTS) is the graph whose vertex set is composed of the blocks of the TTS and two vertices are joined by an edge if…