广义θ-图的分数关联色数

On Fractional Incidence Chromatic Number of Generalized θ-graph

本文从分数色数的定义和已有结论出发,针对两种不同的情况分别给出广义θ-图的分数关联色数,并由此进一步给出广义θ-图的r-冠图的分数关联色数,得到如下结论:incf(θk)={k+1,至少有一条路径的长不为2k2k-1,所有路径的长均为2;incf(Ir(θk))=inc(Ir(θk))=k+r+1。

The issue of coloring is a very important in the graph theory.Fractional coloring as generalized coloring has used in many fields of computer science.This paper compute the fractional incidence chromatic number of generalized θ-graph from to two different situations and using its definition and given lemma.Then,the fractional incidence chromatic number of r-corona graph for generalized θ-graph is obtained.The main results we give as follows：1） incf（θk）={k＋1,at least one path from u to v has longth≠2k2k-1,otherwise;2） incf（Ir（θk））=inc（Ir（θk））=k＋r＋1.