Discrete Mathematics & Theoretical Computer Science, Vol 12, No 5 (2010)

Font Size:  Small  Medium  Large

Convex Partitions of Graphs induced by Paths of Order Three

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


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.

Full Text: PDF PostScript