@inproceedings{52395f39a2f14b3b865a9d35b4c81e93,
title = "On the Cop Number of String Graphs",
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 Gaven{\v c}iak 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)].",
keywords = "Cop number, intersection graphs, planar graphs, pursuit-evasion games, string graphs",
author = "Sandip Das and Harmender Gahlawat",
note = "Publisher Copyright: {\textcopyright} Sandip Das and Harmender Gahlawat.; 33rd International Symposium on Algorithms and Computation, ISAAC 2022 ; Conference date: 19-12-2022 Through 21-12-2022",
year = "2022",
month = dec,
day = "1",
doi = "10.4230/LIPIcs.ISAAC.2022.45",
language = "English",
series = "Leibniz International Proceedings in Informatics, LIPIcs",
publisher = "Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing",
editor = "Bae, {Sang Won} and Heejin Park",
booktitle = "33rd International Symposium on Algorithms and Computation, ISAAC 2022",
address = "Germany",
}