منابع مشابه
Equistable series-parallel graphs
A graph is called equistable when there is a non-negative 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 characterize those series-parallel graphs that are equistable, generalizing results of Mahadev, Peled and Sun about equistable outer-planar graphs.
متن کاملEquistable Chordal Graphs
A graph is called equistable when there is a non-negative 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 chordal graphs is equistable if and only if every two adjacent non-simplicial vertices have a common simplicial neighbor.
متن کاملEquistable distance-hereditary graphs
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 distanceheredita...
متن کاملRecognizing k-equistable Graphs in FPT Time
A graph G = (V,E) is called equistable if there exist a positive integer t and a weight function w : V → N such that S ⊆ V is a maximal stable set of G if and only if w(S) = t. Such a function w is called an equistable function of G. For a positive integer k, a graph G = (V,E) is said to be k-equistable if it admits an equistable function which is bounded by k. We prove that the problem of reco...
متن کاملEquistarable graphs and counterexamples to three conjectures on equistable graphs
Equistable graphs are graphs admitting positive weights on vertices such that a subset of vertices is a maximal stable set if and only if it is of total weight 1. In 1994, Mahadev et al. introduced a subclass of equistable graphs, called strongly equistable graphs, as graphs such that for every c ≤ 1 and every non-empty subset T of vertices that is not a maximal stable set, there exist positive...
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ژورنال
عنوان ژورنال: Discrete Applied Mathematics
سال: 2003
ISSN: 0166-218X
DOI: 10.1016/s0166-218x(03)00397-4