Acyclic List Colouring Locally Planar Graphs
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866913609645293568 |
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| author | Postle, Luke Smith-Roberge, Evelyne Vicenzo, Massimo |
| author_facet | Postle, Luke Smith-Roberge, Evelyne Vicenzo, Massimo |
| contents | A (vertex) colouring of graph is \emph{acyclic} if it contains no bicoloured cycle. In 1979, Borodin proved that planar graphs are acyclically 5-colourable. In 2010, Kawarabayashi and Mohar proved that locally planar graphs are acyclically 7-colourable. In 2002, Borodin, Fon-Der-Flaass, Kostochka, Raspaud, and Sopena proved that planar graphs are acyclically 7-list-colourable. We prove that locally planar graphs are acyclically 9-list-colourable\textemdash no bound for acyclic list colouring locally planar graphs for any fixed number of colours was previously known. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2412_09410 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Acyclic List Colouring Locally Planar Graphs Postle, Luke Smith-Roberge, Evelyne Vicenzo, Massimo Combinatorics A (vertex) colouring of graph is \emph{acyclic} if it contains no bicoloured cycle. In 1979, Borodin proved that planar graphs are acyclically 5-colourable. In 2010, Kawarabayashi and Mohar proved that locally planar graphs are acyclically 7-colourable. In 2002, Borodin, Fon-Der-Flaass, Kostochka, Raspaud, and Sopena proved that planar graphs are acyclically 7-list-colourable. We prove that locally planar graphs are acyclically 9-list-colourable\textemdash no bound for acyclic list colouring locally planar graphs for any fixed number of colours was previously known. |
| title | Acyclic List Colouring Locally Planar Graphs |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2412.09410 |