图与超图中的彩色匹配综述

超图H=(V,E)是一个二元组(V,E),其中超边集E中的元素是点集V的非空子集.因此图是一种特殊的超图,超图也可以看作是一般图的推广.特别地,如果超边集E中的元素均是点集V的k元子集,则称该超图为k-一致的.通常情况下,为叙述简便,我们也会将超边简称为边.图(超图)中的匹配是指图(超图)中互不相交的边的集合.对于图(超图)中的彩色匹配,有两种定义方式:一为染色图(超图)中互不相交且颜色不同的边的集合;二为顶点集均为n]的多个染色图(超图)所构成的集族中互不相交且颜色均不同的边的集合,且每条边均来自集族中不同的图(超图).现主要介绍了图与超图中关于彩色匹配的相关结果.

A survey on rainbow matchings in graphs and hypergraphs

A hypergraph H=(V, E) is a two-tuple (V, E), where the element in the hyperedge set E is a non-empty subset of the vertex set V. Therefore, the graph is a special hypergraph, and the hypergraph can also be regarded as a generalization of the general graph. In particular, if the elements in the hyperedge set E are all a k-subset of the vertex set V, then the hypergraph is said to be k-uniform. Usually, for the sake of simplicity, we will also refer to the hyperedge as the edge. A matching in a graph (hypergraph) refers to a collection of mutually disjoint edges in a graph (hypergraph). There are two ways to define a rainbow matching:one is a collection of mutually disjoint edges with different colors in an edge-colored graph(hypergraph); the other one is a collection of mutually disjoint edges with different colors, where each edge is from different edge-colored graphs(hypergraphs). This paper mainly introduces the results related to rainbow matchings in graphs and hypergraphs.