On the Cop Number of String Graphs

Sandip Das, Harmender Gahlawat

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

1 Scopus citations


Cops and Robber is a well-studied two-player pursuit-evasion game played on a graph, where a group of cops tries to capture the robber. The cop number of a graph is the minimum number of cops required to capture the robber. We show that the cop number of a string graph is at most 13, improving upon a result of Gavenčiak et al. [Eur. J. of Comb. 72, 45–69 (2018)]. Using similar techniques, we also show that four cops have a winning strategy for a variant of Cops and Robber, named Fully Active Cops and Robber, on planar graphs, addressing an open question of Gromovikov et al. [Austr. J. Comb. 76(2), 248–265 (2020)].

Original languageEnglish
Title of host publication33rd International Symposium on Algorithms and Computation, ISAAC 2022
EditorsSang Won Bae, Heejin Park
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Electronic)9783959772587
StatePublished - 1 Dec 2022
Event33rd International Symposium on Algorithms and Computation, ISAAC 2022 - Virtual, Online, Korea, Republic of
Duration: 19 Dec 202221 Dec 2022

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
ISSN (Print)1868-8969


Conference33rd International Symposium on Algorithms and Computation, ISAAC 2022
Country/TerritoryKorea, Republic of
CityVirtual, Online


  • Cop number
  • intersection graphs
  • planar graphs
  • pursuit-evasion games
  • string graphs

ASJC Scopus subject areas

  • Software


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