The board / combinatorics / #780
Erdős Problem #780
PROVEDdatabase updated 2025-08-31
The statement as posed is true, and a proof exists.
What the community database records, not our verdict. erdosproblems.com no longer shows statuses (why).
Suppose \(n\geq kr+(t-1)(k-1)\) and the edges of the complete \(r\)-uniform hypergraph on \(n\) vertices are \(t\)-coloured. Prove that some colour class must contain \(k\) pairwise disjoint edges. In other words, this problem asks to determine the chromatic number of the Kneser hypergraph. When \(k=2\) this was conjectured by Kneser and proved by Lovász [Lo78]. The general case was proved by Alon, Frankl, and Lovász [AFL86].
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research solved. The authoritative wording is on erdosproblems.com/780.Prizenone
Topicscombinatorics, hypergraphs, chromatic number
Statement in LeanFormal Conjectures
Solution in Leanno
Original pageerdosproblems.com/780
Attempts
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