### 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 language | English |
---|---|

Pages (from-to) | 28-32 |

Number of pages | 5 |

Journal | European Journal of Combinatorics |

Volume | 32 |

Issue number | 1 |

DOIs | |

Publication status | Published - Jan 1 2011 |

### ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics

## Fingerprint Dive into the research topics of 'Optimal guard sets and the Helly property'. Together they form a unique fingerprint.

## Cite this

Bacsó, G., & Tuza, Z. (2011). Optimal guard sets and the Helly property.

*European Journal of Combinatorics*,*32*(1), 28-32. https://doi.org/10.1016/j.ejc.2010.08.001