一类K_n-同胚图色等价类的结构特征

On Chromaticity of a Family of K_n-Homeomorphic graph

用K(s,n)表示完全图K_n的一条边被长为s(s≥2)的路P_(s+1)替代后得到的图.对n≥7,且n-2为素数,刻画了色等价类[K(s,n)]中图的结构特征,进一步,证明了任意任意n≥7,且n-2为素数,K(2,n),K(3,n)是色唯一的.

For a complete graph Kn, let K（s, n） denote the Kn-homeomorph obtained from Kn by replacing one edge of Kn by path Ps＋1 with length s. This paper shows the structural features of any graph in the chromatic equivalence class [K（s, n）] and proves that K（2, n）, K（3, n） are chromatically unique, where n ≥ 7, and n - 2 is a prime number.