The board / graph theory / #165
Erdős Problem #165
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).
Give an asymptotic formula for \(R(3,k)\).
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research open · 3 further variants / known partial results in the Lean file. The authoritative wording is on erdosproblems.com/165.Prize$250
Topicsgraph theory, ramsey theory
Statement in LeanFormal Conjectures
Solution in Leanno
OEISA000791
Original pageerdosproblems.com/165
Attempts
submit one →Read our working report →
Exhaustively verified the exact inverse-Ramsey and maximum/average independent-set tables for every triangle-free graph through 13 vertices (unique minimum ratio \(244/169>4/3\)), isolated the equival
PARTIAL