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COMBINATORICS
2006

Total Domination and Matching Numbers in Claw-Free Graphs

8 years 11 months ago
Total Domination and Matching Numbers in Claw-Free Graphs
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 K1,3 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.
Michael A. Henning, Anders Yeo
Added 11 Dec 2010
Updated 11 Dec 2010
Type Journal
Year 2006
Where COMBINATORICS
Authors Michael A. Henning, Anders Yeo
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