Cops and Robbers on Intersection Graphs

  • Tomás Gavenčiak
  • Vít Jelínek
  • Pavel Klavík
  • Jan Kratochvíl
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8283)

Abstract

The game of cops and robber, introduced by Nowakowski and Winkler in 1983, is played by two players on a graph G, one controlling k cops and the other one robber, all positioned on VG. The players alternate in moving their pieces to distance at most 1 each. The cops win if they capture the robber, the robber wins by escaping indefinitely. The cop-number of G, that is the smallest k such that k cops win the game, has recently been a widely studied parameter.

Intersection graph classes are defined by their geometric representations: the vertices are represented by certain geometrical shapes and two vertices are adjacent if and only if their representations intersect. Some well-known intersection classes include interval and string graphs. Various properties of many of these classes have been studied recently, including an interest in their game-theoretic properties.

In this paper we show an upper bound on the cop-number of string graphs and sharp bounds on the cop-number of interval filament graphs, circular graphs, circular arc graphs and function graphs. These results also imply polynomial algorithms determining cop-number for all these classes and their sub-classes.

Keywords

intersection graphs string graphs interval filament graphs cop and robber pursuit games games on graphs 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Tomás Gavenčiak
    • 1
  • Vít Jelínek
    • 2
  • Pavel Klavík
    • 2
  • Jan Kratochvíl
    • 1
  1. 1.Department of Applied Mathematics, Faculty of Mathematics and PhysicsCharles UniversityPragueCzech Republic
  2. 2.Computer Science Institute, Faculty of Mathematics and PhysicsCharles UniversityPragueCzech Republic

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