Partial domination - the isolation number of a graph

Abstract

We prove the following result: If G be a connected graph on n ? 6 vertices, then there exists a set of vertices D with ?D?? n/3 and such that V(G) n N[D] is an independent set, where N[D] is the closed neighborhood of D. Furthermore, the bound is sharp. This seems to be the first result in the direction of partial domination with constrained structure on the graph induced by the non-dominated vertices, which we further elaborate in this paper.