Pathwidth of cubic graphs and exact algorithms - Fomin, Fedor V.; Høie, Kjartan (Information processing letters, 2006)
We prove that for any ɛ > 0 there exists an integer n ɛ such that the pathwidth of every cubic (or 3-regular) graph on n > n ɛ vertices is at most ( 1 / 6 + ɛ ) 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.