Thomassé's 8-edge-connected antisymmetric 5-flow conjecture
Thomassé's 8-edge-connected antisymmetric 5-flow conjecture
Let be a directed graph. An antisymmetric -flow is a -flow in which no two arcs receive inverse elements of ; in particular, it is nowhere-zero when . Thomassé's conjecture. Every directed -edge-connected graph has a -antisymmetric flow. The source presents this as an open conjecture, motivated by the dual relationship with homomorphisms of planar graphs and by the existence of directed -edge-connected graphs without a -antisymmetric flow.
Sources & referencesView supporting material
Primary source
Louis Esperet, Rémi de Joannis de Verclos, Tien-Nam Le and Stéphan Thomassé, “Additive bases and flows in graphs”, arXiv:1701.03366 (2018).
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