Improved Bounds on the Cop Number of a Graph Drawn on a Surface

Joshua Erde*, Florian Lehner

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference paperpeer-review

Abstract

It is known that the cop number c(G) of a connected graph G can be bounded as a function of the genus of the graph g(G). It is conjectured by Schröder that c(G) ≤ g(G) + 3. Recently, by relating this problem to a topological game, the authors, together with Bowler and Pitz, gave the current best known bound that c(G)≤4g(G)3+103. Combining some of these ideas with some techniques introduced by Schröder we improve this bound and show that c(g)≤(1+o(1))(3-3)g≈1.268g.

Original languageEnglish
Title of host publicationTrends in Mathematics
Subtitle of host publicationExtended Abstracts EuroComb 2021
PublisherSpringer
Pages111-116
Number of pages6
Volume14
DOIs
Publication statusPublished - 2021
EventEuropean Conference on Combinatorics, Graph Theory and Applications: EuroComb 2021 - Online, Virtual, Barcelona, Spain
Duration: 6 Sep 202110 Sep 2021

Publication series

NameTrends in Mathematics
Volume14
ISSN (Print)2297-0215
ISSN (Electronic)2297-024X

Conference

ConferenceEuropean Conference on Combinatorics, Graph Theory and Applications
Country/TerritorySpain
CityVirtual, Barcelona
Period6/09/2110/09/21

Keywords

  • Cops and Robbers
  • Genus
  • Graph searching

ASJC Scopus subject areas

  • Mathematics(all)

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