Thomassé's 8-edge-connected antisymmetric 5-flow conjecture

Let G\vec{G} be a directed graph. An antisymmetric BB-flow is a BB-flow in which no two arcs receive inverse elements of BB; in particular, it is nowhere-zero when 0=00=-0. Thomassé's conjecture. Every directed 88-edge-connected graph has a Z5\mathbb{Z}_5-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 77-edge-connected graphs without a Z5\mathbb{Z}_5-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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