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As a natural generalization of chromatic number of a graph, the circularchromatic number of graphs (or the star chromatic number) was introduced byA.Vince in 1988. Let $M^t(G)$ denote the $t$th iterated Mycielski graph of $G$.It was conjectured by Chang, Huang and Zhu(Discrete mathematics,205(1999),23-37) that for all $n \ge t+2, \chi_c(M^t(K_n))=\chi(M^t(K_n))=n+t.$ In 2004,D.D.F. Liu proved the conjecture when $t\ge 2$, $n\ge 2^{t-1}+2t-2$. In thispaper,we show that the result can be strengthened to the following: if $t\ge4$, $n\ge {11/12}2^{t-1}+2t+{1/3}$, then $\chi_c(M^t(K_n))=\chi(M^t(K_n))$.

The Circular Chromatic Number of the Mycielskian of Mt(Kn)