Archdeacon–Jaeger oriented 5-cycle double cover conjecture

Let GG be a bridgeless graph. An oriented 5-cycle double cover is a collection of five directed cycles such that every edge of GG belongs to exactly two cycles and the two cycles traverse that edge in opposite directions.

Archdeacon–Jaeger's oriented 5-cycle double cover conjecture. Every bridgeless graph GG has an oriented 5-cycle double cover.

The conjecture is presented as an implication used to obtain the bound ϕ2(G)τ2\phi_2(G)\leq \tau^2, where τ\tau is the Golden Ratio; its resolution is not specified in the source.

Sources & referencesView supporting material

Primary source

Davide Mattiolo, Giuseppe Mazzuoccolo, Jozef Rajník and Gloria Tabarelli, “Geometric description of d-dimensional flows of a graph”, arXiv:2510.19411 (2025).

Additional references

2 papers in this index state this conjecture (2023–2025). The statement above is taken from the most recent of them; the others are arXiv:2304.14231.

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