【摘 要】
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图G的一个k-全染色是指用k种颜色对图的顶点和边进行染色,使得相邻或者相关联的两个元素染不同的颜色。使图G存在一个k-全染色的最小整数k称为图G的全色数,记为x"(G)。全
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图G的一个k-全染色是指用k种颜色对图的顶点和边进行染色,使得相邻或者相关联的两个元素染不同的颜色。使图G存在一个k-全染色的最小整数k称为图G的全色数,记为x"(G)。全染色问题是图染色的基本问题之一,Behzad和Vizing分别提出了著名的全染色猜想：对任意单图G,x"(G)≤△+2,其中△表示图G的最大长度。许多图论学者对该问题都进行过研究并取得了大量的结果。对一般图,此猜想已经证明对△≤5的图是成立的。
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