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.

Source : oai:HAL:hal-00990463v1

Volume: Vol. 12 no. 5

Section: Graph and Algorithms

Published on: January 1, 2010

Submitted on: March 26, 2015

Keywords: graph convexity,convex partition,[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]

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