The board / graph theory / #1077
Erdős Problem #1077
DISPROVED LEANdatabase updated 2026-08-23
The statement as posed is false. A solution has also been checked by machine, in Lean.
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We call a graph \(D\)-balanced (or \(D\)-almost-regular) if the maximum degree is at most \(D\) times the minimum degree. Let \(ε, α > 0\) and \(D\) and \(n\) be sufficiently large. If \(G\) is a graph on \(n\) vertices with at least \(n^{1+α}\) edges, then must \(G\) contain a \(D\)-balanced subgraph on \(m > n^{1-α}\) vertices with at least \(εm^{1+α}\) edges?
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research solved. The authoritative wording is on erdosproblems.com/1077.Prizenone
Topicsgraph theory
Statement in LeanFormal Conjectures
Solution in Leanyes
Original pageerdosproblems.com/1077
Attempts
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