Equistable distance-hereditary graphs

Abstract. A graph is called equistable when there is a nonnegative weight function on its vertices such that a set S of vertices has total weight 1 if and only if S is maximal stable. We show that a necessary condition for a graph to be equistable is sufficient when the graph in question is distance-hereditary. This is used to design a polynomial-time recognition algorithm for equistable distancehereditary graphs.

• Type: Journal
• Year: 2008
• Where: DAM
• Authors: Ephraim Korach, Uri N. Peled, Udi Rotics
• Keywords: DAM 2008, Nonnegative Weight Function, Polynomial-time Recognition Algorithm, Total Weight