Archdeacon's 5-oriented-cycle-double-cover conjecture

An oriented kk-cycle double-cover (or kk-OCDC) of a graph is a multiset of kk oriented cycles in which every edge occurs in each orientation in exactly one cycle.

Archdeacon's conjecture. Every bridgeless graph has a 55-OCDC.

The conjecture is part of the cycle-double-cover approach to nowhere-zero flow problems. The supplied text states that it is not known whether every bridgeless graph has a kk-OCDC for some kk, so this specific assertion remains open.

Sources & referencesView supporting material

Primary source

Lukáš Gáborik, Sascha Kurz, Giuseppe Mazzuoccolo, Jozef Rajník and Florian Rieg, “Manhattan and Chebyshev flows”, arXiv:2510.22234 (2025).

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