Rainbow even cycles
Fuente:
arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866913331768459264 |
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| author | Dong, Zichao Xu, Zijian |
| author_facet | Dong, Zichao Xu, Zijian |
| contents | We prove that every family of (not necessarily distinct) even cycles $D_1, \dotsc, D_{\lfloor 1.2(n-1) \rfloor+1}$ on some fixed $n$-vertex set has a rainbow even cycle (that is, a set of edges from distinct $D_i$'s, forming an even cycle). This resolves an open problem of Aharoni, Briggs, Holzman and Jiang. Moreover, the result is best possible for every positive integer $n$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2211_09530 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Rainbow even cycles Dong, Zichao Xu, Zijian Combinatorics 05C35, 05C38 We prove that every family of (not necessarily distinct) even cycles $D_1, \dotsc, D_{\lfloor 1.2(n-1) \rfloor+1}$ on some fixed $n$-vertex set has a rainbow even cycle (that is, a set of edges from distinct $D_i$'s, forming an even cycle). This resolves an open problem of Aharoni, Briggs, Holzman and Jiang. Moreover, the result is best possible for every positive integer $n$. |
| title | Rainbow even cycles |
| topic | Combinatorics 05C35, 05C38 |
| url | https://arxiv.org/abs/2211.09530 |