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Convex Partitions of Graphs induced by Paths of Order Three

Abstract : 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.
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C. C. Centeno, S. Dantas, M. C. Dourado, Dieter Rautenbach, Jayme Luiz Szwarcfiter. Convex Partitions of Graphs induced by Paths of Order Three. Discrete Mathematics and Theoretical Computer Science, DMTCS, 2010, 12 (5), pp.175-184. ⟨hal-00990463⟩

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