### Convex Partitions of Graphs induced by Paths of Order Three

*C. C. Centeno, S. Dantas, M. C. Dourado, Dieter Rautenbach, Jayme Luiz Szwarcfiter*

#### Abstract

A set C of vertices of a graph G is
P

_{3}-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 P_{3}-convex sets. Furthermore, we study such partitions for a variety of graph classes.Full Text: PDF PostScript