Pré-Publication, Document De Travail Année : 2022

The bondage number of chordal graphs

Résumé

A set SV(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 AE(G) such that γ(GA)=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.

Dates et versions

hal-03612990 , version 1 (18-03-2022)

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Valentin Bouquet. The bondage number of chordal graphs. 2022. ⟨hal-03612990⟩
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