On the maximum stable set of a permutation graph

Abstract

. . . . 7r j[ is the position in the sequence where the number i can be found [3]. Any vertex adjacent to vertex i is said to be dominated by i while any other vertex is independent(stable) of i. A subset of the vertices of a graph G = (V,E) is a stable set if no two vertices in the subset are adjacent. A stable set is maximal if any vertex not in the set is dominated by at least one vertex in it. 1(G) is the cardinality of maximum stable set. Permutation graphs were introduced by Even and Pnnueli in 1971 [4]. They also showed the transitivity of permutation graphs and an 0(n2) algorithm to find a maximum stable set [1]. In [3] Golumbic showed an 0(n log n) algorithm to find the chromatic number C(G). The domination problems in permutation graphs were studied by Farber and Keil [2]. They presented an 0(n2) algorithm to find a minimum dominating set.