Borel Kernels in Borel Directed Graphs
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866911719075348480 |
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| author | Wang, Ruijun |
| author_facet | Wang, Ruijun |
| contents | We prove that there is a Borel quasi-kernel in any locally countable Borel directed graph with finite Borel chromatic number. We prove that the Borel chromatic number of a Borel directed graph with bounded out-degree $n$ is either infinite or less than or equal to $\frac{(n+1)(n+2)}{2}$. This is an alternative proof of Palamourdas' theorem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_01948 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Borel Kernels in Borel Directed Graphs Wang, Ruijun Logic Combinatorics Primary 03E15, Secondary 05C15, 05C20, 05C69 We prove that there is a Borel quasi-kernel in any locally countable Borel directed graph with finite Borel chromatic number. We prove that the Borel chromatic number of a Borel directed graph with bounded out-degree $n$ is either infinite or less than or equal to $\frac{(n+1)(n+2)}{2}$. This is an alternative proof of Palamourdas' theorem. |
| title | Borel Kernels in Borel Directed Graphs |
| topic | Logic Combinatorics Primary 03E15, Secondary 05C15, 05C20, 05C69 |
| url | https://arxiv.org/abs/2509.01948 |