Bounded persistence pathwidth

Authors:
Rodney G. Downey;Catherine McCartin
Affiliations:
Victoria University, Wellington, New Zealand;Massey University, Palmerston North, New Zealand
Venue:
CATS '05 Proceedings of the 2005 Australasian symposium on Theory of computing - Volume 41
Year:
2005

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Abstract

The role of graph width metrics, such as treewidth, pathwidth, and cliquewidth, is now seen as central in both algorithm design and the delineation of what is algorithmically possible. In this article we introduce a new, related, parameter for graphs, persistence.A path decomposition of width k, in which every vertex of the underlying graph belongs to at most l nodes of the path, has pathwidth k and persistence l, and a graph that admits such a decomposition has bounded persistence pathwidth.We believe that this natural notion truly captures the intuition behind the notion of pathwidth. We present some basic results regarding the general recognition of graphs having bounded persistence path decompositions.