Showing papers on "Dominating set published in 1976"
TL;DR: An algorithm is presented which finds a maximum independent set in an n-vertex graph in 0($2^{n/3}$) time and can thus handle graphs roughly three times as large as could be analyzed using a naive algorithm.
Abstract: We present an algorithm which finds a maximum independent set in an n-vertex graph in 0($2^{n/3}$) time. The algorithm can thus handle graphs roughly three times as large as could be analyzed using a naive algorithm.
489 citations
TL;DR: A linear algorithm to find a minimum 1-basis (a minimum dominating set) when G is a tree and a linear algorithm that solves the problem for any forest is presented.
Abstract: The problem of finding a minimum k-basis of graph G is that of selecting as small a set B of vertices as possible such that every vertex of G is at distance k or less from some vertex in B. Cockayne, Goodman, and Hedetniemi previously developed a linear algorithm to find a minimum 1-basis (a minimum dominating set) when G is a tree. In this paper the k-basis problem is placed in a more general setting, and a linear algorithm is presented that solves the problem for any forest.
115 citations
TL;DR: A new parameter, the maximum number of disjoint independent dominating sets in G, is studied and the class of graphs whose vertex sets partition intoindependent dominating sets is investigated.
45 citations