Circular chromatic number for iterated Mycielski graphs

For a graph G, let M(G) denote the Mycielski graph of G. The tth iterated Mycielski graph of G, M(t)(G), is defined recursively by M(0)(G) = G, and M(t)(G) = M(M(t-1)(G)) for t greater than or equal to 1. Let chi(c)(G) denote the circular chromatic number of G. We prove two main results: (1) If G has a universal vertex x, then chi(c)(M(G)) = chi(M(G)) if chi(c)(G - x) > chi(G) - 1/2 and G is not a star, other-wise chi(c)(M(G)) = chi(M(G)) - 1/2; and (2) chi(c)(M(t)(K(m))) = chi(M(t)(K(m))) if m greater than or equal to 2(t-1) + 2t - 2 and t greater than or equal to 2. (C) 2004 Elsevier B.V. All rights reserved.