On the Cop Number of String Graphs
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)].
Cop number
string graphs
intersection graphs
planar graphs
pursuit-evasion games
Mathematics of computing~Graph algorithms
45:1-45:18
Regular Paper
This research was financed by the IFCAM project "Applications of graph homomorphisms" (MA/IFCAM/18/39).
We thank Uma kant Sahoo, Dibyayan Chakraborty, and Florent Foucaud for initial discussions on the topic of this paper.
Sandip
Das
Sandip Das
Indian Statistical Institute, Kolkata, India
Harmender
Gahlawat
Harmender Gahlawat
Ben-Gurion University of the Negev, Beer-Sheva, Israel
https://sites.google.com/view/harmendergahlawat/
https://orcid.org/0000-0001-7663-6265
Supported by the Israel Science Foundation (ISF) grant no. 1176/18
10.4230/LIPIcs.ISAAC.2022.45
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Sandip Das and Harmender Gahlawat
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