License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ISAAC.2022.45
URN: urn:nbn:de:0030-drops-173308
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2022/17330/
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Das, Sandip ; Gahlawat, Harmender

On the Cop Number of String Graphs

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LIPIcs-ISAAC-2022-45.pdf (0.9 MB)

Abstract

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)].

BibTeX - Entry

@InProceedings{das_et_al:LIPIcs.ISAAC.2022.45,
  author =	{Das, Sandip and Gahlawat, Harmender},
  title =	{{On the Cop Number of String Graphs}},
  booktitle =	{33rd International Symposium on Algorithms and Computation (ISAAC 2022)},
  pages =	{45:1--45:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-258-7},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{248},
  editor =	{Bae, Sang Won and Park, Heejin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2022/17330},
  URN =		{urn:nbn:de:0030-drops-173308},
  doi =		{10.4230/LIPIcs.ISAAC.2022.45},
  annote =	{Keywords: Cop number, string graphs, intersection graphs, planar graphs, pursuit-evasion games}
}

Keywords: Cop number, string graphs, intersection graphs, planar graphs, pursuit-evasion games
Collection: 33rd International Symposium on Algorithms and Computation (ISAAC 2022)
Issue Date: 2022
Date of publication: 14.12.2022

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