Convex partitions of graphs induced by paths of order three

Abstract

A set C of vertices of a graph G is P3-convex if v ∈ C for every path uvw in G with u,w ∈ C. We prove that it is NP-complete to decide for a given graph G and a given integer p whether the vertex set of G can be partitioned into p non-empty disjoint P3-convex sets. Furthermore, we study such partitions for a variety of graph classes. © 2010 Discrete Mathematics and Theoretical Computer Science (DMTCS).