Pathwidth of cubic graphs and exact algorithms

Authors:
Fedor V. Fomin;Kjartan Høie
Affiliations:
Department of Informatics, University of Bergen, Bergen, Norway;Department of Informatics, University of Bergen, Bergen, Norway
Venue:
Information Processing Letters
Year:
2006

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Abstract

We prove that for any ε 0 there exists an integer nε such that the pathwidth of every cubic (or 3-regular) graph on n nε vertices is at most (1/6 + ε)n. Based on this bound we improve the worst case time analysis for a number of exact exponential algorithms on graphs of maximum vertex degree three.