Bounding the cop number of a graph by its genus

Joshua Erde, Florian Lehner, Max Pitz, Nathan Bowler

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

The game of cops and robbers is a pursuit game played on a graph G in which a group of cops tries to catch a robber, where both are allowed to move along to edges of G. The cop number of G, denoted by c(G), is the smallest number of cops needed to catch a robber on G. Schröder showed that c(G) is at most 3/2 g(G) + 3, where g(G) is the genus of G, that is, the smallest k such that G can be drawn on an orientable surface of genus k. Furthermore, he conjectured that this bound could be improved to g(G) +3. By relating the game of cops and robbers to a topological game played on a surface we prove that c(G) is at most 4/3 g(G) +3.
Original languageEnglish
Title of host publicationProceedings of the European Conference on Combinatorics, Graph Theory and Applications (EuroComb 2019)
Pages507-510
Publication statusPublished - 2019

Publication series

NameActa Mathematica Universitatis Comenianae

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