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 mappingσfrom 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.