G. MacGillivray

collaborators

2 papers

math.CO2025

Hamiltonicity of Bell and Stirling Colour Graphs

Stephen Finbow, Gary MacGillivray

For a graph $G$ and a positive integer $k$ , the $k$ -Bell colour graph of $G$ is the graph whose vertices are the partitions of $V$ into at most $k$ independent sets, with two of th…

math.CO2025

Bounding the Eviction Number of a Graph in Terms of its Independence Number

Gary MacGillivray, Christina Mynhardt, Virgelot Virgile

An eternal dominating family of graph $G$ in the eviction game is a collection $D_{k} = {D_{1}, ..., D_{l}}$ of dominating sets of $G$ such that (a) $∣ D_{i} ∣ = ∣ D_{j} ∣$ for a…