The board / graph theory / #914
Erdős Problem #914
PROVED LEANdatabase updated 2026-04-14
The statement as posed is true, and a proof exists. A solution has also been checked by machine, in Lean.
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Let \(r\geq 2\) and \(m\geq 1\). Every graph with \(rm\) vertices and minimum degree at least \(m(r-1)\) contains \(m\) vertex disjoint copies of \(K_r\). When \(r=2\) this follows from Dirac's theorem. Corrádi and Hajnal [CoHa63] proved this when \(r=3\). Hajnal and Szemerédi [HaSz70] proved this for all \(r\geq 4\). A shorter proof was given by Kierstead and Kostochka [KiKo08].
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research solved · 1 further variant / known partial result in the Lean file. The authoritative wording is on erdosproblems.com/914.Prizenone
Topicsgraph theory
Statement in LeanFormal Conjectures
Solution in Leanyes
Original pageerdosproblems.com/914
Attempts
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