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Article Dans Une Revue Graphs and Combinatorics Année : 2010

Paired-domination in subdivided star-free graphs

Paul Dorbec
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Sylvain Gravier

Résumé

A set S of vertices in a graph G is a paired-dominating set of G if every vertex of G is adjacent to some vertex in S and if the subgraph induced by S contains a perfect matching. The paired-domination number of G is the minimum cardinality of a paired-dominating set of G. Dorbec, Gravier and Henning gave tight bounds for paired-dominating sets of generalized claw-free graphs. Yet, the critical cases are not claws but subdivided stars. We here give a bound for graphs containing no induced subdivided stars, depending on the size of the star.
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Dates et versions

hal-00522607 , version 1 (01-10-2010)

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  • HAL Id : hal-00522607 , version 1

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Paul Dorbec, Sylvain Gravier. Paired-domination in subdivided star-free graphs. Graphs and Combinatorics, 2010, 26 (1), pp.43-49. ⟨hal-00522607⟩
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