彩虹不连通染色数

Rainbow Disconnection Coloring Number

摘要: 设G是一个非平凡的边染色连通图，如果图G的一个边割R中没有任何两条边是相同的颜色，则称R是图G的一个彩虹边割。u和v是图G的任意两个不相同的顶点，如果图G的一个彩虹边割R满足u和v属于$G-R$ 的不同连通分支，则称图G的这个边染色为彩虹不连通染色。本文主要对图的彩虹不连通染色已有的结论进行综述，并讨论了一些结论之间的关系。

Abstract: Let G be a nontrivial connected, edge-colored graph, and an edge-cut R of G is called a rainbow cut if no two edges in R are colored the same. An edge-coloring of G is a rainbow disconnection coloring if for every two distinct vertices u and v of G, there exists a rainbow cut in G, where u and v belong to different components of $G-R$ . In this paper, we summerize the results for rainbow disconnection colorings in graph, and the relationship between some conclusions is discussed.