Total domination and matching numbers in claw-free graphs
The electronic journal of combinatorics, Tome 13 (2006)
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.
@article{10_37236_1085,
author = {Michael A. Henning and Anders Yeo},
title = {Total domination and matching numbers in claw-free graphs},
journal = {The electronic journal of combinatorics},
year = {2006},
volume = {13},
doi = {10.37236/1085},
zbl = {1100.05071},
url = {http://geodesic.mathdoc.fr/articles/10.37236/1085/}
}
Michael A. Henning; Anders Yeo. Total domination and matching numbers in claw-free graphs. The electronic journal of combinatorics, Tome 13 (2006). doi: 10.37236/1085
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