The board / graph theory / #82
Erdős Problem #82
OPENdatabase updated 2025-08-31
No proof or disproof is known, and it isn't known whether a finite computation could settle it.
What the community database records, not our verdict. erdosproblems.com no longer shows statuses (why).
A predicate that holds if \(S\) is a regular induced subgraph of \(G\)
\(F(n)\) is the maximal integer such that every graph on \(n\) vertices contains a regular induced subgraph on at least \(F(n)\) vertices.
\(F(n) / \log n \to \infty as n \to \infty\)
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research open · 1 further variant / known partial result in the Lean file. The authoritative wording is on erdosproblems.com/82.Prizenone
Topicsgraph theory
Statement in LeanFormal Conjectures
Solution in Leanno
OEISA120414, A390256, A390257, A390919, A392636, A394400, A394462, A394539, A394563, A394564, A394573, A394574, A394930, A394933
Original pageerdosproblems.com/82
Attempts
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Live page status OPEN; collision rule triggered because “Currently working on this problem” lists Svyable (checked 2026-07-27).
SKIPPED