The bondage number of chordal graphs
Résumé
A set S⊆V(G) of a graph G is a dominating set if each vertex has a neighbor in S or belongs to S. Let γ(G) be the cardinality of a minimum dominating set in G. The bondage number b(G) of a graph G is the smallest cardinality of a set edges A⊆E(G) such that γ(G−A)=γ(G)+1. A chordal graph is a graph with no induced cycle of length four or more. In this paper, we prove that the bondage number of a chordal graph G is at most the order of its maximum clique, that is, b(G)≤ω(G). We show that this bound is best possible.