Paired-domination in subdivided star-free graphs
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.