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Cop and robber games when the robber can hide and ride

Jérémie Chalopin 1, Victor Chepoi 1, Nicolas Nisse 2, Yann Vaxès 1

(2010-01)

In the classical cop and robber game, two players, the cop C and the robber R, move alternatively along edges of a finite graph G=(V,E). The cop captures the robber if both players are on the same vertex at the same moment of time. A graph G is called cop win if the cop always captures the robber after a finite number of steps. Nowakowski, Winkler (1983) and Quilliot (1983) characterized the cop-win graphs as graphs admitting a dismantling scheme. In this paper, we characterize in a similar way the cop-win graphs in the game in which the cop and the robber move at different speeds s' and s, s'<= s. We also investigate several dismantling schemes necessary or sufficient for the cop-win graphs in the game in which the robber is visible only every k moves for a fixed integer k>1. We characterize the graphs which are cop-win for any value of k.

1:	Laboratoire d'informatique Fondamentale de Marseille (LIF)
	CNRS : UMR6166 – Université de la Méditerranée - Aix-Marseille II – Université de Provence - Aix-Marseille I
2:	MASCOTTE (INRIA Sophia Antipolis / Laboratoire I3S)
	INRIA – Université Nice Sophia Antipolis [UNS] – CNRS : UMR7271

Domain

:

Computer Science/Discrete Mathematics

Keywords: Cops and Robber games – dismantling ordering – hyperbolicity

inria-00448243, version 3

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From: Nicolas Nisse <>

Submitted on: Monday, 25 January 2010 18:01:20

Updated on: Friday, 5 February 2010 11:54:53