Three Theorems on Negami's Planar Cover Conjecture
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866913627662974976 |
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| author | Annor, Dickson Nikolayevsky, Yuri Payne, Michael |
| author_facet | Annor, Dickson Nikolayevsky, Yuri Payne, Michael |
| contents | A long-standing Conjecture of S. Negami states that a connected graph has a finite planar cover if and only if it embeds in the projective plane. It is known that the Conjecture is equivalent to the fact that \emph{the graph $K_{1,2, 2, 2}$ has no finite planar cover}. We prove three theorems showing that the graph $K_{1,2, 2, 2}$ admits no planar cover with certain structural properties, and that the minimal planar cover of $K_{1,2, 2, 2}$ (if it exists) must be $4$-connected. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_19560 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Three Theorems on Negami's Planar Cover Conjecture Annor, Dickson Nikolayevsky, Yuri Payne, Michael Combinatorics A long-standing Conjecture of S. Negami states that a connected graph has a finite planar cover if and only if it embeds in the projective plane. It is known that the Conjecture is equivalent to the fact that \emph{the graph $K_{1,2, 2, 2}$ has no finite planar cover}. We prove three theorems showing that the graph $K_{1,2, 2, 2}$ admits no planar cover with certain structural properties, and that the minimal planar cover of $K_{1,2, 2, 2}$ (if it exists) must be $4$-connected. |
| title | Three Theorems on Negami's Planar Cover Conjecture |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2412.19560 |