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Mathematics > Combinatorics

arXiv:1910.14200 (math)
[Submitted on 31 Oct 2019 (v1), last revised 5 Aug 2021 (this version, v2)]

Title:Cops that surround a robber

Authors:Andrea C. Burgess, Rosalind A. Cameron, Nancy E. Clarke, Peter Danziger, Stephen Finbow, Caleb W. Jones, David A. Pike
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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 $\sigma(G)$ the {\em surrounding cop number} of $G$, namely the least number of cops required to surround a robber in the graph $G$. 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.
Subjects: Combinatorics (math.CO); Discrete Mathematics (cs.DM)
Cite as: arXiv:1910.14200 [math.CO]
  (or arXiv:1910.14200v2 [math.CO] for this version)
  https://doi.org/10.48550/arXiv.1910.14200
Related DOI: https://doi.org/10.1016/j.dam.2020.06.019

Submission history

From: Andrea Burgess [view email]
[v1] Thu, 31 Oct 2019 01:14:46 UTC (42 KB)
[v2] Thu, 5 Aug 2021 16:46:29 UTC (26 KB)
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