The five-cycle double cover conjecture

Let GG be a bridgeless cubic graph. A 55-cycle double cover (55-CyDC) is a tuple of five cycles of GG such that every edge belongs to exactly two members of the tuple.

Five-cycle double cover conjecture. Every bridgeless cubic graph has a 55-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).

Progress summary

Never refreshed

Nothing recorded yet. Refresh searches the literature and the public web for attempts on this problem, and writes the first summary here.

Solutions 0

No solutions have been posted yet.