K4-Free Graphs with No Odd Hole: Even Pairs and the Circular Chromatic Number

An odd hole in a graph is an induced cycle of odd length at least five. In this article we show that every imperfect K-4-free graph with no odd hole either is one of two basic graphs, or has an even pair or a clique cutset. We use this result to show that every K-4-free graph with no odd hole has circular chromatic number strictly smaller than 4. We also exhibit a sequence {H-n} of such graphs with lim(n ->infinity) chi(c)(H-n)=4. (C) 2010 Wiley Periodicals, Inc. J Graph Theory 65: 303-322, 2010