Rainbow matchings in edge-colored graphs
Hongliang Lu, Zixuan Yang, and Feihong Yuan

TL;DR
This paper investigates the existence of rainbow matchings of size k in edge-colored graphs, establishing tight conditions based on the sum of edges and colors, extending previous results on rainbow triangles and cliques.
Contribution
It introduces a new tight condition for the existence of rainbow matchings of size k in edge-colored graphs, generalizing prior work on rainbow triangles and cliques.
Findings
Established a tight bound on e(G)+c(G) for rainbow matchings
Extended previous results from triangles and cliques to matchings
Provided a generalized condition applicable to all edge-colored graphs
Abstract
Let be an edge-colored graph. We use and to denote the number of edges and colors in , respectively. A subgraph is called rainbow if . Li et al. (European J. Combin., 36 (2014), 453-459) proved that every edge-colored graph on vertices with contains rainbow triangles. Later, Xu et al. (European J. Combin., 54 (2016), 193-200) generalized the previous results concerning rainbow triangles to rainbow cliques , where . In this paper, we consider the existence of rainbow matchings of size in general edge-colored graphs under the condition of , and the condition in our result is tight.
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Taxonomy
TopicsLimits and Structures in Graph Theory · Advanced Graph Theory Research · graph theory and CDMA systems
