The board / graph theory / #77
Erdős Problem #77
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).
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 find the value of \[\lim_{k\to \infty}R(k)^{1/k}.\] This problem is #3 in Ramsey Theory in the graphs problem collection.
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research open. The authoritative wording is on erdosproblems.com/77.Prize$250
Topicsgraph theory, ramsey theory
Statement in LeanFormal Conjectures
Solution in Leanno
OEISA059442
Original pageerdosproblems.com/77
Attempts
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Live page status “OPEN - $250”; the “Currently working on this problem” marker names Sam_Petkov (fetched via Bright Data on 2026-07-26), so the mandatory non-collision rule applies.
SKIPPED