The Hajnal–Szemerédi theorem on equitable colourings
A Lean 4 / Mathlib formalization of the Hajnal–Szemerédi theorem (1970), conjectured by Erdős in 1964: every finite graph with maximum degree at most r has an equitable proper colouring with r + 1 colours, i.e. a proper colouring whose colour classes differ in size by at most one. The exact form is also proved: if the number of vertices is s(r + 1), every colour class has exactly s vertices (the colouring form of Erdős Problem #914). The proof follows the short argument of Kierstead and Kostochka (2008): induction on the number of edges; after deleting an edge, a nearly equitable colouring…
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