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math.CO2026
Exponentially Many Circuit Double Covers
Radek Hušek, Robert Šámal
The cycle double cover conjecture of Szekeres and Seymour, the proof of which was recently announced by OpenAI, states that every bridgeless graph has a collection of cycles coveri…
math.CO2026
Facial diagrams and cycle double cover
Babak Ghanbari, Robert Šámal
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…
math.CO2025
Approximate cycle double cover
Babak Ghanbari, Robert Šámal
The Cycle double cover (CDC) conjecture states that for every bridgeless graph , there exists a family of cycles such that each edge of the graph is contained in e…