Cops that surround a robber
Combinatorics
2021-08-06 v2 Discrete Mathematics
Abstract
We introduce the game of Surrounding Cops and Robbers on a graph, as a variant of the original game of Cops and Robbers. In contrast to the original game in which the cops win by occupying the same vertex as the robber, they now win by occupying each of the robber's neighbouring vertices. We denote by the {\em surrounding cop number} of , namely the least number of cops required to surround a robber in the graph . We present a number of results regarding this parameter, including general bounds as well as exact values for several classes of graphs. Particular classes of interest include product graphs, graphs arising from combinatorial designs, and generalised Petersen graphs.
Cite
@article{arxiv.1910.14200,
title = {Cops that surround a robber},
author = {Andrea C. Burgess and Rosalind A. Cameron and Nancy E. Clarke and Peter Danziger and Stephen Finbow and Caleb W. Jones and David A. Pike},
journal= {arXiv preprint arXiv:1910.14200},
year = {2021}
}