# 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

## 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 |
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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: | https://eprints.sztaki.hu/id/eprint/6596 |

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