Facial diagrams and cycle double cover
arXiv:2605.014108.3h-index: 2
Predicted impact top 59% in CO · last 90 daysOriginality Synthesis-oriented
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Provides a new approach to a long-standing open problem in graph theory, but the results are theoretical and incremental.
The paper tackles the cycle double cover conjecture for cubic graphs by studying edge twists in 2-cell embeddings on surfaces, deriving bounds on the number of singular edges.
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).