Pathwidth is NP-Hard for Weighted Trees

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.

• Type: Conference
• Year: 2009
• Where: FAW
• Authors: Rodica Mihai, Ioan Todinca
• Keywords: Algorithms, Chordal Graphs, FAW 2009, Minimum Clique Number, Particular Subclasses