## Abstract

For a hypergraph H, the transversal is a subset of vertices whose intersection with every edge is nonempty. The cardinality of a minimum transversal is the transversal number of H, denoted by τ(H). The Tuza constant c_{k} is defined as supτ(H)/(m+n), where H ranges over all k-uniform hypergraphs, with m and n being the number of edges and vertices, respectively. We give an upper bound and a lower bound on c_{k}. The upper bound improves the known ones for k≥7, and the lower bound improves the known ones for k∈{7,8,10,11,13,14,17}.

Original language | English |
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Article number | 113756 |

Journal | Discrete Mathematics |

Volume | 347 |

Issue number | 2 |

DOIs | |

Publication status | Published - 2024 Feb |

## Keywords

- Hypergraph
- Transversal number
- Tuza constant

## ASJC Scopus subject areas

- Theoretical Computer Science
- Discrete Mathematics and Combinatorics

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