{"id":"palomar/PALOMAR-2026-10-13-000007","url":"https://github.com/jtraverso/hajnal-szemeredi/tree/2a71de73134d10cdfecfe52cec652a386f1aa356","json":"https://data.palomar-registry.org/entries/PALOMAR-2026-10-13-000007-v2.json","repo":"https://github.com/jtraverso/hajnal-szemeredi","tags":["math.CO","msc:05C15","msc:05C35"],"score":0,"title":"The Hajnal–Szemerédi theorem on equitable colourings","trust":"high","domain":"math.CO","source":"palomar","authors":["Juan Pablo Traverso Gianini"],"reviews":0,"subject":"math.CO","summary":"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). Version 2 adds the form with any number k > Δ(G) of colours (Mathlib's SimpleGraph.maxDegree), deduced from the theorem with r = k − 1. The proof follows the…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"verified":true,"discussed":0,"published":"2026-10-30","reactions":{},"formalized":true,"formalizes":[{"title":"A short proof of the Hajnal–Szemerédi theorem on equitable colouring","identifier":"doi:10.1017/S0963548307008619","relationship":"formalizes"},{"title":"Proof of a conjecture of P. Erdős","identifier":"","relationship":"formalizes"}]}