Open Research Index

Nowhere-zero 3-flows in 6-edge-connected graphs

Juan Pablo Traverso Gianini

Palomar Registrypalomar/PALOMAR-2026-10-28-000022Oct 28, 2026math.COscore 0

A Lean 4 / Mathlib formalization of the theorem of Lovász, Thomassen, Wu and Zhang: every finite 6-edge-connected simple graph has a nowhere-zero integer 3-flow (the weak 3-flow conjecture). The proof formalizes Theorem 3.1 of the paper (β-orientations of multigraphs modulo 3) and Tutte's lifting theorem. Only simple graphs are stated; the paper's multigraph version and its results on modulo k-orientations for k > 3 are not stated. Mathlib does not contain this theorem.

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