21 citations · 47 across the 15 of their papers we have counts for
5 papers · 1 filter
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…