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Journal Articles Discrete Mathematics and Theoretical Computer Science Year : 2010

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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Dates and versions

hal-00990463 , version 1 (13-05-2014)

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Cite

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, 2010, Vol. 12 no. 5 (5), pp.175-184. ⟨10.46298/dmtcs.502⟩. ⟨hal-00990463⟩

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