Hušek–Šámal's exponential circuit double cover conjecture
Let be a -connected cubic graph on vertices. A circuit double cover (CiDC) is a finite family of connected -regular subgraphs of such that every edge belongs to exactly two members of the family.
Hušek–Šámal's conjecture. The graph has at least
CiDCs.
This is a quantitative strengthening of the cycle double cover problem. The bound is proved in the source for -connected -edge-colorable cubic graphs and is known to be tight for Klee graphs, while the general conjecture remains open.
References
Primary source
Radek Hušek and Robert Šámal, “Exponentially Many Circuit Double Covers”, arXiv:2607.24724 (2026).
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