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arXiv · 2605.01410

Facial diagrams and cycle double cover

Babak Ghanbari·Robert Šámal
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Abstract

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).

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Babak Ghanbari, Robert Šámal. 2026-05-02. Facial diagrams and cycle double cover. https://arxiv.org/abs/2605.01410

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