On the Cop Number of String Graphs
Document Type
Conference Article
Publication Title
Leibniz International Proceedings in Informatics, LIPIcs
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)].
DOI
10.4230/LIPIcs.ISAAC.2022.45
Publication Date
12-1-2022
Recommended Citation
Das, Sandip and Gahlawat, Harmender, "On the Cop Number of String Graphs" (2022). Conference Articles. 374.
https://digitalcommons.isical.ac.in/conf-articles/374
