Facial diagrams and cycle double cover
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866917454382366720 |
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| author | Ghanbari, Babak Šámal, Robert |
| author_facet | Ghanbari, Babak Šámal, Robert |
| contents | We approach the cycle double cover conjecture by looking for a circular 2-cell embedding of cubic graphs on an arbitrary surface. It is easy to see that if such an embedding exists, we can get to it from an arbitrary starting 2-cell embedding by repeating ``twists of an edge''. We study this twisting operation in detail and deduce bounds on the number of singular edges (edges where a face meets itself). |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_01410 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Facial diagrams and cycle double cover Ghanbari, Babak Šámal, Robert Combinatorics Discrete Mathematics We approach the cycle double cover conjecture by looking for a circular 2-cell embedding of cubic graphs on an arbitrary surface. It is easy to see that if such an embedding exists, we can get to it from an arbitrary starting 2-cell embedding by repeating ``twists of an edge''. We study this twisting operation in detail and deduce bounds on the number of singular edges (edges where a face meets itself). |
| title | Facial diagrams and cycle double cover |
| topic | Combinatorics Discrete Mathematics |
| url | https://arxiv.org/abs/2605.01410 |