Density of the circular chromatic numbers of series‐parallel graphs

Suppose Gis a series‐parallel graph. It was proved in 3 that either χc(G) = 3 or χc(G) ≤ 8/3. So none of the rationals in the interval (8/3, 3) is the circular chromatic number of a series‐parallel graph. This paper proves that for every rational r∈ [2, 8/3] ∪ {3} there exists a series‐parallel graph Gwith χc(G) = r. © 2004 Wiley Periodicals, Inc. J Graph Theory 46:57–68, 2004