Open Research Index

Kőnig's theorems and Dilworth's theorem

Juan Pablo Traverso Gianini

Palomar Registrypalomar/PALOMAR-2026-10-15-000019Oct 15, 2026math.COscore 0

A Lean 4 / Mathlib formalization of Kőnig's edge-colouring theorem: the line graph of a finite bipartite graph G is Δ(G)-colourable, and its chromatic number (the chromatic index of G) equals Δ(G). The proof colours edges one at a time with partial proper edge colourings, recolouring by an a/b Kempe-chain swap whose correctness rests on a parity argument in the bipartite graph; the lower bound comes from the edges at a vertex of maximum degree, which are pairwise adjacent in the line graph. Also formalized: the Kőnig–Egerváry theorem (a finite bipartite graph has a matching and a vertex…

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