Convex Partitions of Graphs induced by Paths of Order Three
Carmen Cecilia Centeno, Simone Dantas, Mitre Costa Dourado, Dieter Rautenbach, Jayme Luiz SZWARCFITER · Discrete Mathematics & Theoretical Computer Science · 2010
Graphs and Algorithms A set C of vertices of a graph G is P(3)-convex if v is an element of C for every path uvw in G with u, w is an element of 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 P(3)-convex sets. Furthermore, we study such partitions for a variety of graph classes.