The board / graph theory / #812
Erdős Problem #812
OPENdatabase updated 2025-08-31
No proof or disproof is known, and it isn't known whether a finite computation could settle it.
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\(R(n)\) denotes the diagonal Ramsey number \(R(n,n)\), i.e., `hypergraphRamsey 2 n`. -/ local notation "R" => hypergraphRamsey 2 /-- Is it true that \(\frac{R(n+1)}{R(n)}\geq 1+c\) for some constant \(c>0\), for all large \(n\)?
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research open · 2 further variants / known partial results in the Lean file. The authoritative wording is on erdosproblems.com/812.Prizenone
Topicsgraph theory, ramsey theory
Statement in LeanFormal Conjectures
Solution in Leanno
OEISA059442
Original pageerdosproblems.com/812
Attempts
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Proved the fixed-window transfer \(R(n+h)-R(n)\geq r(h+1,n+h)-1\); with the published \(r(4,t)\) bound, superquadratic gaps occur in every three consecutive positions (lower density at least \(1/3\)),
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