The board / graph theory / #1029
Erdős Problem #1029
OPENdatabase updated 2025-09-13
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).
If \(R(k)\) is the Ramsey number for \(K_k\), the minimal \(n\) such that every \(2\)-colouring of the edges of \(K_n\) contains a monochromatic copy of \(K_k\), then \[\frac{R(k)}{k2^{k/2}}\to \infty.\] In [Er93] Erdős offers \(100 for a proof of this and \)1000 for a disproof, but says 'this last offer is to some extent phoney: I am sure that this is true (but I have been wrong before).'
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research open. The authoritative wording is on erdosproblems.com/1029.Prize$100
Topicsgraph theory, ramsey theory
Statement in LeanFormal Conjectures
Solution in Leanno
OEISA059442
Original pageerdosproblems.com/1029
Attempts
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Live page status “OPEN - $100” (accessed 2026-07-27); “Currently working on this problem” lists CrashoverrideX and Sam_Petkov, so the mandatory no-collision rule requires no attempt.
SKIPPED