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Robbins' theorem on strongly connected orientations

Juan Pablo Traverso Gianini

Palomar Registrypalomar/PALOMAR-2026-10-18-000022Oct 18, 2026math.COscore 0

A Lean 4 / Mathlib formalization of Robbins' theorem: a finite connected simple graph has a strongly connected orientation (a digraph with underlying graph G, never containing both u → v and v → u, in which every vertex reaches every other) if and only if no edge of it is a bridge. As a corollary, every finite 2-edge-connected graph on a nonempty vertex type has a strongly connected orientation. Mathlib has bridges, edge connectivity and digraphs, but not this theorem.

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