## Abstract

A set M of edges of a graph G is a matching if no two edges in M are incident to the same vertex. The matching number of G is the maximum cardinality of a matching of G. A set 5 of vertices in G is a, total dominating set of G if every vertex of G is adjacent to some vertex in S. The minimum cardinality of a total dominating set of G is the total domination number of G. If G does not contain K_{1,3} as an induced subgraph, then G is said to be claw-free. We observe that the total domination number of every claw-free graph with minimum degree at least three is bounded above by its matching number. In this paper, we use transversals in hypergraphs to characterize connected claw-free graphs with minimum degree at least three that have equal total domination and matching numbers.

Original language | English |
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Pages (from-to) | 1-28 |

Number of pages | 28 |

Journal | Electronic Journal of Combinatorics |

Volume | 13 |

Issue number | 1 R |

DOIs | |

Publication status | Published - 28 Jul 2006 |

Externally published | Yes |

## Keywords

- Claw-free
- Matching number
- Total domination number

## ASJC Scopus subject areas

- Theoretical Computer Science
- Geometry and Topology
- Discrete Mathematics and Combinatorics
- Computational Theory and Mathematics
- Applied Mathematics