Some star extremal circulant graphs
The circular chromatic number and the fractional chromatic number are two generalizations of the ordinary chromatic number of a graph \(G\). A graph is called star extremal if its circular chromatic number equals its fractional chromatic number. \textit{G. Gao} and \textit{X. Zhu} [Discrete Math. 152, 147-156 (1996; Zbl 0852.05046)], \textit{K.-W. Lih} et al. [SIAM J. Discrete Math. 12, 491-499 (1999; Zbl 0935.05042)] gave many classes of circulant graphs which are star extremal. In this paper the author studies the star extremality of circulant graphs whose generating sets are of the form \(\{1,2,\dots ,m-1,k,k+1,\dots ,k+m-2\}\), of the form \(\{k,k+1,\dots ,k'\}\), or of the form \(\{k,k+1,\dots ,k_{1},k_{2},k_{2}+1,\dots ,\lfloor p/2 \rfloor \}\), where \(p\) is the order of the graph. As a corollary, an improvement of a result of Gao and Zhu is proposed.
scientific article; zbMATH DE number 1985957