The five-cycle double cover conjecture
The five-cycle double cover conjecture
Let be a bridgeless cubic graph. A -cycle double cover (-CyDC) is a tuple of five cycles of such that every edge belongs to exactly two members of the tuple.
Five-cycle double cover conjecture. Every bridgeless cubic graph has a -CyDC.
The ordinary cycle double cover conjecture is stated in the source as solved, but the five-cycle version remains open. The paper also gives a flow-only formulation of this conjecture and proves related results, including a characterization for a prescribed cycle.
Sources & referencesView supporting material
Primary source
Radek Hušek and Robert Šámal, “Exponentially Many Circuit Double Covers”, arXiv:2607.24724 (2026).
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