Colouring random subgraphs
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2023
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866918077231267840 |
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| author | Bukh, Boris Krivelevich, Michael Narayanan, Bhargav |
| author_facet | Bukh, Boris Krivelevich, Michael Narayanan, Bhargav |
| contents | We study several basic problems about colouring the $p$-random subgraph $G_p$ of an arbitrary graph $G$, focusing primarily on the chromatic number and colouring number of $G_p$. In particular, we show that there exist infinitely many $k$-regular graphs $G$ for which the colouring number (i.e., degeneracy) of $G_{1/2}$ is at most $k/3 + o(k)$ with high probability, thus disproving the natural prediction that such random graphs must have colouring number at least $k/2 - o(k)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_08340 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Colouring random subgraphs Bukh, Boris Krivelevich, Michael Narayanan, Bhargav Combinatorics Probability 05C80, 05C15 We study several basic problems about colouring the $p$-random subgraph $G_p$ of an arbitrary graph $G$, focusing primarily on the chromatic number and colouring number of $G_p$. In particular, we show that there exist infinitely many $k$-regular graphs $G$ for which the colouring number (i.e., degeneracy) of $G_{1/2}$ is at most $k/3 + o(k)$ with high probability, thus disproving the natural prediction that such random graphs must have colouring number at least $k/2 - o(k)$. |
| title | Colouring random subgraphs |
| topic | Combinatorics Probability 05C80, 05C15 |
| url | https://arxiv.org/abs/2312.08340 |