广义 Mycielski 图的边色数

摘要

Letμ1 ( G) denote the Mycielskian of a graph G, the generalized Mycielski graphs μm ( G) were the natural generalization of Mycielski graphs . It was focused on the edge coloring problem of generalized Mycielski graph, and proved that if G was a simple connected graph , other than K2 , thenμm ( G) would be of Class 1, i.e., the edge chromatic number was equal to the maximum degree , m≥2.The proof was based on color switch technique .The results in relevant field were then improved .%设μ1（ G）表示一个图G的Mycielski 图。广义Mycielski图μm （ G）是Mycielski 图μ1（ G）的自然推广。研究广义Mycielski图μm （ G）的边染色问题，运用换色技巧证明了：若G是不同于K2的连通简单图，则对任何m≥2，μm（G）是第一类的，即边色数等于最大度。推广了现有关于Mycielski图的边色数的相关结果。