## Abstract

A transversal in a hypergraph H is set of vertices that intersect every edge of H. A transversal coalition in H consists of two disjoint sets of vertices X and Y of H, neither of which is a transversal but whose union X∪Y is a transversal in H. Such sets X and Y are said to form a transversal coalition. A transversal coalition partition in H is a vertex partition Ψ={V_{1},V_{2},…,V_{p}} such that for all i∈[p], either the set V_{i} is a singleton set that is a transversal in H or the set V_{i} forms a transversal coalition with another set V_{j} for some j, where j∈[p]∖{i}. The transversal coalition number C_{τ}(H) in H equals the maximum order of a transversal coalition partition in H. For k≥2 a hypergraph H is k-uniform if every edge of H has cardinality k. Among other results, we prove that if k≥2 and H is a k-uniform hypergraph, then [Formula presented]. Further we show that for every k≥2, there exists a k-uniform hypergraph that achieves equality in this upper bound.

Original language | English |
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Article number | 114267 |

Journal | Discrete Mathematics |

Volume | 348 |

Issue number | 2 |

DOIs | |

Publication status | Published - Feb 2025 |

## Keywords

- Edge colorings
- Hypergraph
- Latin squares
- Linear intersecting hypergraph
- Transversal

## ASJC Scopus subject areas

- Theoretical Computer Science
- Discrete Mathematics and Combinatorics