Archdeacon's 5-oriented-cycle-double-cover conjecture
Archdeacon's 5-oriented-cycle-double-cover conjecture
An oriented -cycle double-cover (or -OCDC) of a graph is a multiset of oriented cycles in which every edge occurs in each orientation in exactly one cycle.
Archdeacon's conjecture. Every bridgeless graph has a -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 -OCDC for some , 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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