Vizing's theorem and equitable edge colourings
A Lean 4 / Mathlib formalization of Vizing's theorem: every finite simple graph G has a proper edge colouring with Δ(G) + 1 colours, stated with Mathlib's line graph (G.lineGraph is (Δ(G) + 1)-colourable, hence χ'(G) ≤ Δ(G) + 1), proved with fans and Kempe chain exchanges. It also proves the equitable refinement: for every c ≥ Δ(G) + 1 there is a proper edge colouring with colours Fin c in which any two colour classes (including unused colours) differ in size by at most one (McDiarmid 1972), obtained by balancing a Vizing colouring with alternating-component moves that strictly decrease a…
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