### 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 | Discrete Mathematics |

Volume | 86 |

Issue number | 1-3 |

DOIs | |

Publication status | Published - Dec 14 1990 |

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### ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics
- Theoretical Computer Science

### Cite this

*Discrete Mathematics*,

*86*(1-3), 117-126. https://doi.org/10.1016/0012-365X(90)90354-K

**Covering all cliques of a graph.** / Tuza, Z.

Research output: Contribution to journal › Article

*Discrete Mathematics*, vol. 86, no. 1-3, pp. 117-126. https://doi.org/10.1016/0012-365X(90)90354-K

}

TY - JOUR

T1 - Covering all cliques of a graph

AU - Tuza, Z.

PY - 1990/12/14

Y1 - 1990/12/14

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.

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UR - http://www.scopus.com/inward/citedby.url?scp=0002628574&partnerID=8YFLogxK

U2 - 10.1016/0012-365X(90)90354-K

DO - 10.1016/0012-365X(90)90354-K

M3 - Article

VL - 86

SP - 117

EP - 126

JO - Discrete Mathematics

JF - Discrete Mathematics

SN - 0012-365X

IS - 1-3

ER -