### Abstract

The following conjecture of T. Gallai is proved: If G is a chordal graph on n vertices, such that all its maximal complete subgraphs have order at least 3, then there is a vertex set of cardinality ≤n/3 which meets all maximal complete subgraphs of G. Further related results are given.

Original language | English |
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Pages (from-to) | 117-126 |

Number of pages | 10 |

Journal | Annals of Discrete Mathematics |

Volume | 48 |

Issue number | C |

DOIs | |

Publication status | Published - 1991 |

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### ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics

### Cite this

*Annals of Discrete Mathematics*,

*48*(C), 117-126. https://doi.org/10.1016/S0167-5060(08)71043-4

**Covering All Cliques of a Graph.** / Tuza, Z.

Research output: Contribution to journal › Article

*Annals of Discrete Mathematics*, vol. 48, no. C, pp. 117-126. https://doi.org/10.1016/S0167-5060(08)71043-4

}

TY - JOUR

T1 - Covering All Cliques of a Graph

AU - Tuza, Z.

PY - 1991

Y1 - 1991

N2 - The following conjecture of T. Gallai is proved: If G is a chordal graph on n vertices, such that all its maximal complete subgraphs have order at least 3, then there is a vertex set of cardinality ≤n/3 which meets all maximal complete subgraphs of G. Further related results are given.

AB - The following conjecture of T. Gallai is proved: If G is a chordal graph on n vertices, such that all its maximal complete subgraphs have order at least 3, then there is a vertex set of cardinality ≤n/3 which meets all maximal complete subgraphs of G. Further related results are given.

UR - http://www.scopus.com/inward/record.url?scp=77957767702&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77957767702&partnerID=8YFLogxK

U2 - 10.1016/S0167-5060(08)71043-4

DO - 10.1016/S0167-5060(08)71043-4

M3 - Article

VL - 48

SP - 117

EP - 126

JO - Annals of Discrete Mathematics

JF - Annals of Discrete Mathematics

SN - 0167-5060

IS - C

ER -