On improved upper bounds on the transversal number of hypergraphs

Michael A. Henning, Nader Jafari Rad, Hailiza Kamarulhaili, Wen Chean Teh

Research output: Contribution to journalArticlepeer-review

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 languageEnglish
Pages (from-to)350-359
Number of pages10
JournalAustralasian Journal of Combinatorics
Volume85
Publication statusPublished - 2023

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics

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