## Abstract

A subset T of vertices in a hypergraph H is a transversal if T has a nonempty intersection with every edge of H. The transversal number of H is the minimum size of a transversal in H. A subset S of vertices in a graph G with no isolated vertex is a total dominating set if every vertex of G is adjacent to a vertex of S. The minimum cardinality of a total dominating set in G is the total domination number of G. In this note, we improve previous probabilistic upper bounds given for the transversal number of a hypergraph and the total domination number of a graph given by the first two authors in [Discrete Math. Algorithms Appl. 11 (1) (2019), 1950004, 6 pp.].

Original language | English |
---|---|

Pages (from-to) | 350-359 |

Number of pages | 10 |

Journal | Australasian Journal of Combinatorics |

Volume | 85 |

Publication status | Published - 2023 |

## ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics