图与超图中的彩色匹配综述

doi:10.15960/j.cnki.issn.1007-6093.2019.03.006

摘要/Abstract

摘要： 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.

关键词: 图, 超图, 匹配, 彩色匹配

Abstract: 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.

Key words: graph, hypergraph, matching, rainbow matching

中图分类号:

O157.5

李瞳, 王光辉, 周文玲. 图与超图中的彩色匹配综述[J]. 运筹学学报（中英文）, 2019, 23(3): 77-90.

LI Tong, WANG Guanghui, ZHOU Wenling. A survey on rainbow matchings in graphs and hypergraphs[J]. Operations Research Transactions, 2019, 23(3): 77-90.

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