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{\bf Michael A. Henning and Anders Yeo}
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{\bf Total Domination and Matching Numbers in Claw-Free Graphs}
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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 $S$ 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.
\bye