Optimal guard sets and the Helly property

Gábor Bacsó, Zsolt Tuza

Research output: Contribution to journalArticle

1 Citation (Scopus)

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.

Original languageEnglish
Pages (from-to)28-32
Number of pages5
JournalEuropean Journal of Combinatorics
Volume32
Issue number1
DOIs
Publication statusPublished - Jan 1 2011

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics

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