The board / graph theory / #555
Erdős Problem #555
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 symmetric edge-colouring of the complete graph on \(m\) vertices with \(k\) colours.
The adjacency relation of the cycle \(C_{2n}\) on vertices \(0,\ldots,2n-1\).
A monochromatic copy of a graph with adjacency predicate `Adj`.
Let \(R_k(G)\) be the least \(m\) such that every \(k\)-colouring of the edges of \(K_m\) contains a monochromatic copy of \(G\). Determine \(R_k(C_{2n})\).
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research open. The authoritative wording is on erdosproblems.com/555.Prizenone
Topicsgraph theory, ramsey theory
Statement in LeanFormal Conjectures
Solution in Leanno
OEISA389313
Original pageerdosproblems.com/555
Attempts
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The live page status is OPEN and lists RobSneiderman under “Currently working on this problem” (with 0 claimed proofs), so the mandatory no-collision rule requires stopping.
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