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- Title
A note on improved upper bounds on the transversal number of hypergraphs.
- Authors
Henning, Michael A.; Rad, Nader Jafari
- 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 paper, we obtain a new (improved) probabilistic upper bound for the transversal number of a hypergraph, and a new (improved) probabilistic upper bound for the total domination number of a graph.
- Subjects
HYPERGRAPHS; TRANSVERSAL lines; BOREL subsets; GEOMETRIC vertices; GRAPH theory
- Publication
Discrete Mathematics, Algorithms & Applications, 2019, Vol 11, Issue 1, pN.PAG
- ISSN
1793-8309
- Publication type
Article
- DOI
10.1142/S1793830919500046