Vertex covers and eternal dominating sets
Document Type
Article
Publication Date
5-1-2012
Abstract
The eternal domination problem requires a graph to be protected against an infinitely long sequence of attacks on vertices by guards located at vertices, the configuration of guards inducing a dominating set at all times. An attack at a vertex with no guard is defended by sending a guard from a neighboring vertex to the attacked vertex. We allow any number of guards to move to neighboring vertices at the same time in response to an attack. We compare the eternal domination number with the vertex cover number of a graph. One of our main results is that the eternal domination number is less than the vertex cover number of any graph of minimum degree at least two having girth at least nine. © 2011 Elsevier B.V. All rights reserved.
Publication Title
Discrete Applied Mathematics
Volume
160
Issue
7-8
First Page
1183
Last Page
1190
Digital Object Identifier (DOI)
10.1016/j.dam.2011.11.034
ISSN
0166218X
Citation Information
Klostermeyer, & Mynhardt, C. . (2012). Vertex covers and eternal dominating sets. Discrete Applied Mathematics, 160(7-8), 1183–1190. https://doi.org/10.1016/j.dam.2011.11.034