Facial diagrams and cycle double cover
Combinatorics
2026-05-05 v1 Discrete Mathematics
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).
Cite
@article{arxiv.2605.01410,
title = {Facial diagrams and cycle double cover},
author = {Babak Ghanbari and Robert Šámal},
journal= {arXiv preprint arXiv:2605.01410},
year = {2026}
}