21 citations · 47 across the 15 of their papers we have counts for
16 papers
Distance-Restricted Firefighting on Finite Graphs
Andrea C. Burgess, John Hawkin, Alexander Howse +2
In the classic version of the game of firefighter, on the first turn a fire breaks out on a vertex in a graph and then firefighters protect vertices. On each subsequent…
Existential Closure in Line Graphs
Andrea C. Burgess, Robert D. Luther, David A. Pike
A graph is {\it -existentially closed} if, for all disjoint sets of vertices and with , there is a vertex not in adjacent to each vertex o…
The Edge-Connectivity of Vertex-Transitive Hypergraphs
Andrea C. Burgess, Robert D. Luther, David A. Pike
A graph or hypergraph is said to be vertex-transitive if its automorphism group acts transitively upon its vertices. A classic theorem of Mader asserts that every connected vertex-…
Colourings of path systems
Iren Darijani, David A. Pike
A path in a graph is a path on vertices. A system of order is a partition of the edges of the complete graph into paths. A system is said to…
Firefighting with a Distance-Based Restriction
Andrea Burgess, John Marcoux, David Pike
In the classic version of the game of firefighter, on the first turn a fire breaks out on a vertex in a graph and then firefighters protect vertices. On each subsequent…
Mutually orthogonal cycle systems
Andrea C. Burgess, Nicholas J. Cavenagh, David A. Pike
An -cycle system of a graph is a set of -cycles which partition the edge set of . Two such cycle systems and ar…
Acyclic polynomials of graphs
Caroline Barton, Jason I. Brown, David A. Pike
For each nonnegative integer , let be the number of -subsets of that induce an acyclic subgraph of a given graph . We define $A(G,x) = \sum_{i \geq 0} a_i x^i…
Colourings of star systems
Iren Darijani, David Pike
An -star is a complete bipartite graph . An -star system of order , , is a partition of the edges of the complete graph into -stars. An -sta…
Cops that surround a robber
Andrea C. Burgess, Rosalind A. Cameron, Nancy E. Clarke +4
We introduce the game of Surrounding Cops and Robbers on a graph, as a variant of the original game of Cops and Robbers. In contrast to the original game in which the cops win by o…
The Firebreak Problem
Kathleen D. Barnetson, Andrea C. Burgess, Jessica Enright +3
Suppose we have a network that is represented by a graph . Potentially a fire (or other type of contagion) might erupt at some vertex of . We are able to respond to this outb…
A Perfect One-Factorisation of
David A. Pike
In 1963, Anton Kotzig conjectured that for each the complete graph has a perfect one-factorisation (i.e., a decomposition into perfect matchings such that each…
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…
Twofold triple systems with cyclic 2-intersecting Gray codes
Aras Erzurumluoğlu, David A. Pike
Given a combinatorial design with block set , the block-intersection graph (BIG) of is the graph that has as its vertex set,…
Connectivity in Hypergraphs
Megan Dewar, David Pike, John Proos
In this paper we consider two natural notions of connectivity for hypergraphs: weak and strong. We prove that the strong vertex connectivity of a connected hypergraph is bounded by…
Brushing Number and Zero-Forcing Number of Graphs and their Line Graphs
Aras Erzurumluoglu, David Pike, Karen Meagher
In this paper we compare the brushing number of a graph with the zero-forcing number of its line graph. We prove that the zero-forcing number of the line graph is an upper bound fo…
On balanced incomplete block designs with specified weak chromatic number
Daniel Horsley, David A. Pike
A weak -colouring of a balanced incomplete block design (BIBD) is a colouring of the points of the design with colours in such a way that no block of the design has all of i…