1 citations · 1 across the 3 of their papers we have counts for
6 papers
A Counterexample to an Eternal Domination Conjecture
Tom Adamczewski, William F. Klostermeyer
A graph with 243 vertices is shown having , disproving the Gamma-Theta conjecture for eternal dominating sets.
Eternal Domination in Trees
William F. Klostermeyer, Gary MacGillivray
Mobile guards on the vertices of a graph are used to defend the graph against an infinite sequence of attacks on vertices. A guard must move from a neighboring vertex to an attacke…
The Eternal Game Chromatic Number of a Graph
William Klostermeyer, Hannah Mendoza
Game coloring is a well-studied two-player game in which each player properly colors one vertex of a graph at a time until all the vertices are colored. An `eternal' version of gam…
Disjoint Dominating Sets with a Perfect Matching
William F. Klostermeyer, Margaret-Ellen Messinger, Alejandro Angeli Ayello
In this paper, we consider dominating sets and such that and are disjoint and there exists a perfect matching between them. Let denote the ca…
Domination, Eternal Domination, and Clique Covering
William F Klostermeyer, Christina M Mynhardt
Eternal and m-eternal domination are concerned with using mobile guards to protect a graph against infinite sequences of attacks at vertices. Eternal domination allows one guard to…
Protecting a Graph with Mobile Guards
William F. Klostermeyer, Christina M. Mynhardt
Mobile guards on the vertices of a graph are used to defend it against attacks on either its vertices or its edges. Various models for this problem have been proposed. In this surv…