4 papers
Locally Semi-Equitable Colourings of BIBDs
Andrea C. Burgess, William Kellough, David A. Pike
We study -colourings of -BIBDs (balanced incomplete block designs) where, within each block, one colour is absent and each of the other colours appears exac…
On graph automorphisms related to Snort
Rylo Ashmore, Beth Ann Austin, Alfie M. Davies +2
We study the outcomes of various positions of the game Snort. When played on graphs admitting an automorphism of order two that maps vertices outside of their closed neighbourhoods…
Cops against a cheating robber
Nancy E. Clarke, Danny Dyer, William Kellough
We investigate a cheating robot version of Cops and Robber, first introduced by Huggan and Nowakowski, where both the cops and the robber move simultaneously, but the robber is all…
Eternally surrounding a robber
Nancy E. Clarke, Danny Dyer, William Kellough
We introduce the bodyguard problem for graphs. This is a variation of Surrounding Cops and Robber but, in this model, a smallest possible group of bodyguards must surround the pres…