Open Research Index

The Gallai–Hasse–Roy–Vitaver theorem

Juan Pablo Traverso Gianini

Palomar Registrypalomar/PALOMAR-2026-10-16-000015Oct 16, 2026math.COscore 0

A Lean 4 / Mathlib formalization of the Gallai–Hasse–Roy–Vitaver theorem: if an orientation of a finite graph has no directed path on more than k vertices, the graph is k-colourable; and conversely every k-colourable graph has such an orientation. Hence the chromatic number is the minimum over orientations of the number of vertices of a longest directed path.

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