Circular chromatic number for iterated Mycielski graphs Original Research Article

For a graph G, let M(G) denote the Mycielski graph of G. The tth iterated Mycielski graph of G, Mt(G), is defined recursively by M0(G)=G, and Mt(G)=M(Mt−1(G)) for t⩾1. Let χc(G) denote the circular chromatic number of G. We prove two main results: (1) If G has a universal vertex x, then χc(M(G))=χ(M(G)) if χc(G−x)>χ(G)−12 and G is not a star, otherwise χc(M(G))=χ(M(G))−12; and (2) χc(Mt(Km))=χ(Mt(Km)) if m⩾2t−1+2t−2 and t⩾2.