Star extremal circulant graphs

A graph is called star extremal if its fractional chromatic number is equal to its circular chromatic number (also known as the star chromatic number) . We prove that members of a certain family of circulant graphs are star ex tremal. The result generalizes some known theorems of Sidorenko [Discrete M ath., 91 (1991), pp. 215-217] and Gao and Zhu [Discrete Math., 152 (1996), pp. 147-156]. We show relations between circulant graphs and distance graph s and discuss their star extremality. Furthermore, we give counterexamples to two conjectures of Collins [SIAM J. Discrete Math., 11 (1998), pp. 330-3 39] on asymptotic independence ratios of circulant graphs.