On a recolouring version of Hadwiger's conjecture
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2021
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| _version_ | 1866909536388907008 |
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| author | Bonamy, Marthe Heinrich, Marc Legrand-Duchesne, Clément Narboni, Jonathan |
| author_facet | Bonamy, Marthe Heinrich, Marc Legrand-Duchesne, Clément Narboni, Jonathan |
| contents | We prove that for any $\varepsilon>0$, for any large enough $t$, there is a graph $G$ that admits no $K_t$-minor but admits a $(\frac32-\varepsilon)t$-colouring that is "frozen" with respect to Kempe changes, i.e. any two colour classes induce a connected component. This disproves three conjectures of Las Vergnas and Meyniel from 1981. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2103_10684 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | On a recolouring version of Hadwiger's conjecture Bonamy, Marthe Heinrich, Marc Legrand-Duchesne, Clément Narboni, Jonathan Combinatorics Discrete Mathematics We prove that for any $\varepsilon>0$, for any large enough $t$, there is a graph $G$ that admits no $K_t$-minor but admits a $(\frac32-\varepsilon)t$-colouring that is "frozen" with respect to Kempe changes, i.e. any two colour classes induce a connected component. This disproves three conjectures of Las Vergnas and Meyniel from 1981. |
| title | On a recolouring version of Hadwiger's conjecture |
| topic | Combinatorics Discrete Mathematics |
| url | https://arxiv.org/abs/2103.10684 |