{"id":"palomar/PALOMAR-2026-10-13-000007","url":"https://github.com/jtraverso/hajnal-szemeredi/tree/ba34061e3cf12dfc8297610d5d7b3f0afac7ec54","json":"https://data.palomar-registry.org/entries/PALOMAR-2026-10-13-000007-v1.json","repo":"https://github.com/jtraverso/hajnal-szemeredi","tags":["math.CO","msc:05C15","msc:05C35","graph-theory","equitable-coloring","lean"],"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). 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…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"verified":true,"discussed":0,"published":"2026-10-13","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"}]}