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A New Characterization of Pk-free Graphs

par Camby, Eglantine ;Schaudt, Oliver
Référence Algorithmica, 71, 2, page (1-13)
Publication Publié, 2015-03-24

Article révisé par les pairs

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Résumé :

Let G be a connected Pk-free graph, k≥ 4. We show that G admits a connected dominating set that induces either a Pk- 2-free graph or a graph isomorphic to Pk- 2. In fact, every minimum connected dominating set of G has this property. This yields a new characterization for Pk-free graphs: a graph G is Pk-free if and only if each connected induced subgraph of G has a connected dominating set that induces either a Pk- 2-free graph, or a graph isomorphic to Ck. We present an efficient algorithm that, given a connected graph G, computes a connected dominating set X of G with the following property: for the minimum k such that G is Pk-free, the subgraph induced by X is Pk- 2-free or isomorphic to Pk- 2. As an application our results, we prove that Hypergraph 2-Colorability can be solved in polynomial time for hypergraphs whose vertex-hyperedge incidence graphs is P7-free.