3 papers
math.CO2026
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 exa…
math.CO2025
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…
math.CO2025
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…