星和轮的Mycielski图的{r,s，t}色数

The[r,s,t]Chromatic Number of Mycielski Graph of Star and Wheel

给定非负整数r,s和t,若图G(V,E)有一个映射σ:V∪E→{0,1,…,k-1},k∈N,满足对V中相邻的点v_i,v_j有|σ(v_i)-σ(v_j)|≥r;对E中相邻的边e_i,e_j有|σ(e_i)-σ(e_j)|≥s;对V∪E中相关联的点v_i和边e_j有|σ(v_i)-σ(e_j)|≥t,则称σ为G的一个[r,s,t]-着色.使得图G存在使用了k种颜色的[r,s,t]-着色的最小整数k称为G的[r,s,t]-色数.研究星和轮的Mycielski图的[r,s,t]-着色,并给出其在一定条件下的[r,s,t]-色数.

Given non- negative integers r, s, and t, an [r, s, t]-coloring of a graph G = （V, E） is a mapping σ from VUE to the color set {0, 1, 2, .. , k-l} such that [σ（vi） - σ（vj）] ≥ r for every two adjacent vertices vi, vj, [σ（ei） - σ（ej）] ≥s for every two adjacent edge ei, ej, and [σ（vi） -σ（ej）] ≥ t for all pairs of incident vertices and edges, respectively. The [r, s, t]- chromatic number Xr,s,t（G） of G is defined to be the minimum k such that G admits an [r, s, t]-coloring using k colors . This paper give the [r, s, t]-chromatic number of Mycielski graph of star and wheel if r, s, t meet certain conditions.