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Operations Research Transactions >

2019 , Vol. 23 >Issue 3: 77 - 90

DOI: https://doi.org/10.15960/j.cnki.issn.1007-6093.2019.03.006

A survey on rainbow matchings in graphs and hypergraphs

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  • School of Mathematics, Shandong University, Jinan 250100, China

Received date: 2019-06-25

  Online published: 2019-09-09

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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

Cite this article

LI Tong, WANG Guanghui, ZHOU Wenling . A survey on rainbow matchings in graphs and hypergraphs[J]. Operations Research Transactions, 2019 , 23(3) : 77 -90 . DOI: 10.15960/j.cnki.issn.1007-6093.2019.03.006

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