Connected Graph Searching in Chordal Graphs

Nicolas Nisse 1
1 MASCOTTE - Algorithms, simulation, combinatorics and optimization for telecommunications
CRISAM - Inria Sophia Antipolis - Méditerranée , Laboratoire I3S - COMRED - COMmunications, Réseaux, systèmes Embarqués et Distribués
Abstract : Graph searching was introduced by Parson [T. Parson, Pursuit-evasion in a graph, in: Theory and Applications of Graphs, in: Lecture Notes in Mathematics, Springer-Verlag, 1976, pp. 426--441]: given a “contaminated” graph G (e.g., a network containing a hostile intruder), the search number View the MathML source of the graph G is the minimum number of searchers needed to “clear” the graph (or to capture the intruder). A search strategy is connected if, at every step of the strategy, the set of cleared edges induces a connected subgraph. The connected search number View the MathML source of a graph G is the minimum k such that there exists a connected search strategy for the graph G using at most k searchers. This paper is concerned with the ratio between the connected search number and the search number. We prove that, for any chordal graph G of treewidth View the MathML source, View the MathML source. More precisely, we propose a polynomial-time algorithm that, given any chordal graph G, computes a connected search strategy for G using at most View the MathML source searchers. Our main tool is the notion of connected tree-decomposition. We show that, for any connected graph G of chordality k, there exists a connected search strategy using at most View the MathML source searchers where T is an optimal tree-decomposition of G.
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https://hal.archives-ouvertes.fr/hal-00421414
Contributor : Nicolas Nisse <>
Submitted on : Friday, October 2, 2009 - 12:56:33 AM
Last modification on : Monday, November 5, 2018 - 3:36:03 PM

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Nicolas Nisse. Connected Graph Searching in Chordal Graphs. Discrete Applied Mathematics, Elsevier, 2009, 157 (12), pp.2603-2610. ⟨10.1016/j.dam.2008.08.007⟩. ⟨hal-00421414⟩

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