Rainbow matchings in edge-colored graphs
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866915602604490752 |
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| author | Lu, Hongliang Yang, Zixuan Yuan, Feihong |
| author_facet | Lu, Hongliang Yang, Zixuan Yuan, Feihong |
| contents | Let $G$ be an edge-colored graph. We use $e(G)$ and $c(G)$ to denote the number of edges and colors in $G$, respectively. A subgraph $H$ is called rainbow if $c(H)=e(H)$. Li et al. (European J. Combin., 36 (2014), 453-459) proved that every edge-colored graph on $n$ vertices with $e(G)+c(G) \geq n(n+1)/2$ contains rainbow triangles. Later, Xu et al. (European J. Combin., 54 (2016), 193-200) generalized the previous results concerning rainbow triangles to rainbow cliques $Kr$, where $r\geq 4$. In this paper, we consider the existence of rainbow matchings of size $k$ in general edge-colored graphs $G$ under the condition of $e(G)+c(G)$, and the condition in our result is tight. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2511_04374 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Rainbow matchings in edge-colored graphs Lu, Hongliang Yang, Zixuan Yuan, Feihong Combinatorics Let $G$ be an edge-colored graph. We use $e(G)$ and $c(G)$ to denote the number of edges and colors in $G$, respectively. A subgraph $H$ is called rainbow if $c(H)=e(H)$. Li et al. (European J. Combin., 36 (2014), 453-459) proved that every edge-colored graph on $n$ vertices with $e(G)+c(G) \geq n(n+1)/2$ contains rainbow triangles. Later, Xu et al. (European J. Combin., 54 (2016), 193-200) generalized the previous results concerning rainbow triangles to rainbow cliques $Kr$, where $r\geq 4$. In this paper, we consider the existence of rainbow matchings of size $k$ in general edge-colored graphs $G$ under the condition of $e(G)+c(G)$, and the condition in our result is tight. |
| title | Rainbow matchings in edge-colored graphs |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2511.04374 |