Pathwidth is NP-Hard for Weighted Trees

Rodica Mihai (1) , Ioan Todinca (2)

1 UiB - Department of Informatics [Bergen]
2 LIFO - Laboratoire d'Informatique Fondamentale d'Orléans

The pathwidth of a graph G is the minimum clique number of H minus one, over all interval supergraphs H of G. We prove in this paper that the pathwidth problem is NP-hard for particular subclasses of chordal graphs, and we deduce that the problem remains hard for weighted trees. We also discuss subclasses of chordal graphs for which the problem is polynomial.

Mots clés: pathwidth; weighted trees

Domaines: Algorithme et structure de données [cs.DS]

Rodica Mihai, Ioan Todinca. Pathwidth is NP-Hard for Weighted Trees. Frontiers in Algorithmics, Third International Workshop (FAW 2009), Jun 2009, Hefei, China. pp.181-195, ⟨10.1007/978-3-642-02270-8_20⟩. ⟨hal-00462314⟩