Optimal guard sets and the Helly property

Bacsó, Gábor and Tuza, Zsolt (2011) Optimal guard sets and the Helly property. EUROPEAN JOURNAL OF COMBINATORICS, 32 (1). pp. 28-32. ISSN 0195-6698

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Abstract

In a set system F, a guard set of an F∈F is a subset B⊂F such that B intersects all those F'∈F which meet F but are not contained in F. Given a graph G, we consider set systems F whose intersection graph is G, and determine one such F in which the guard sets of all F∈F are as small as possible. We prove that the minimum-both in global and local sense-is attained by the dual of the clique hypergraph of G, a structure which also played an important role in the proof of the Perfect Graph Theorem. We also put some remarks concerning algorithmic complexity. © 2010 Elsevier Ltd.

Item Type: ISI Article
Subjects: Q Science > QA Mathematics and Computer Science > QA75 Electronic computers. Computer science / számítástechnika, számítógéptudomány
Divisions: Laboratory of Parallel and Distributed Systems
Depositing User: EPrints Admin
Date Deposited: 12 Dec 2012 08:40
Last Modified: 05 Feb 2014 15:47
URI: http://eprints.sztaki.hu/id/eprint/6596

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