一类G_k(a,b;c,d)图的着色

The chromaticity of a family of G_k(a,b;c,d) graphs

令Gk(a,b;c,d)表示θ(a,b,c+k)∪Pd(d≥2),其中Pd 的一个端点与θ(a,b,c+k)的一个3度点u重合,Pd 的另一个端点w 在Pc+k 上,且Pc+k 上w 与θ(a,b,c+ k)的另一个3度点v间的路长为k。给出了G2(m,m;m,m)(m≥2)的着色。

Let G_k(a,b;c,d) denote a 2-connected graph obtained from the disjoint union θ(a,b,c+k)∪p_d(d≥2) by identifying the first vertex of the path P_d with the degree-three vertex u of θ(a,b,c+k)and the last vertex of P_d with a vertex w of p_(c+k) such that the length of the path (on p_(c+k))between w and the other degree-three vertex v of θ(a,b,c+k) is k. The chromaticity of graph G_2(m,m;m,m) is provided.