Density of the circular chromatic numbers of series‐parallel graphs

In this paper we show that every simple cubic graph on n vertices has a set of at least ? n/4 ? disjoint 2‐edge paths and that this bound is sharp. Our proof provides a polynomial time algorithm for finding such a set in a simple cubic graph. © 2003 Wiley Periodicals, Inc. J Graph Theory 45: 57–79, 2003