Séminaire Lotharingien de Combinatoire, B10l (1984), 5 pp.
[Formerly: Publ. I.R.M.A. Strasbourg, 1987, 340/S-10, p. 48-52.]

Daniel I. A. Cohen

Counting Stable Sets in Trees

Abstract. Cook [1] has shown that the problem of generating all the stable sets of a given graph is NP complete while several authors have shown that it is possible to generate all the maximal stable sets of G in polynomial-time. In [3] this is done in O(n = number of vertices, m = number of edges, μ = number of maximal stable sets). In this paper we shall
  1. prove that the problem of counting all stable sets in a tree is no harder than listing all maxima! stable sets in a tree
  2. calculate the upper bound on the number of maxima) stable sets in a tree of n vertices.

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