Pathwidth is NP-Hard for Weighted Trees

Authors:
Rodica Mihai;Ioan Todinca
Affiliations:
Department of Informatics, University of Bergen, Bergen, Norway N-5020;LIFO, Université d'Orléans, Orléans Cedex 2, France 45067
Venue:
FAW '09 Proceedings of the 3d International Workshop on Frontiers in Algorithmics
Year:
2009

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Abstract

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.