### Abstract

We investigate the relations among the chromatic index q(H), the maximum degree Δ(H), the total chromatic number q^{*}(H), and the maximum size Δ_{0}(H) of an intersecting subhypergraph of a hypergraph H. For some particular classes of hypergraphs, including Steiner systems, we provide sufficient conditions insuring that some (or all) of the trivial inequalities Δ(H)≤Δ_{0}(H)≤q(H)≤q^{*}(H turn to equality. For instance, we prove that Δ(H)= Δ_{0}(H) holds whenever the maximum degree of a hypergraph H is sufficiently large with respect to the rank and the 'pair-degree' of H.

Original language | English |
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Pages (from-to) | 79-86 |

Number of pages | 8 |

Journal | Discrete Mathematics |

Volume | 124 |

Issue number | 1-3 |

DOIs | |

Publication status | Published - Jan 1 1994 |

### ASJC Scopus subject areas

- Theoretical Computer Science
- Discrete Mathematics and Combinatorics

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## Cite this

Gionfriddo, M., & Tuza, Z. (1994). On conjectures of Berge and Chvátal.

*Discrete Mathematics*,*124*(1-3), 79-86. https://doi.org/10.1016/0012-365X(94)90086-8