On the anti-Ramsey threshold
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866916553462644736 |
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| author | Kuperwasser, Eden |
| author_facet | Kuperwasser, Eden |
| contents | We say that a graph $G$ is anti-Ramsey for a graph $H$ if any proper edge-colouring of $G$ yields a rainbow copy of $H$, i.e. a copy of $H$ whose edges all receive different colours. In this work we determine the threshold at which the binomial random graph becomes anti-Ramsey for any fixed graph $H$, given that $H$ is sufficiently dense. Our proof employs a graph decomposition lemma in the style of the Nine Dragon Tree theorem that may be of independent interest. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_03439 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the anti-Ramsey threshold Kuperwasser, Eden Combinatorics 05C80, 05D10 We say that a graph $G$ is anti-Ramsey for a graph $H$ if any proper edge-colouring of $G$ yields a rainbow copy of $H$, i.e. a copy of $H$ whose edges all receive different colours. In this work we determine the threshold at which the binomial random graph becomes anti-Ramsey for any fixed graph $H$, given that $H$ is sufficiently dense. Our proof employs a graph decomposition lemma in the style of the Nine Dragon Tree theorem that may be of independent interest. |
| title | On the anti-Ramsey threshold |
| topic | Combinatorics 05C80, 05D10 |
| url | https://arxiv.org/abs/2501.03439 |