The board / graph theory / #569
Erdős Problem #569
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).
Let \(k\geq 1\). What is the best possible \(c_k\) such that \[R(C_{2k+1},H)\leq c_k m\] for any graph \(H\) on \(m\) edges without isolated vertices? This problem is #34 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/569.Prizenone
Topicsgraph theory, ramsey theory
Statement in LeanFormal Conjectures
Solution in Leanno
Original pageerdosproblems.com/569
Attempts
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The live page status is OPEN, but it lists 1 claimed proof—a full proof by Cambie Stijn and Freschi Andrea (arXiv:2606.11174, submitted 2026-07-25)—and its newest comment says the solution is availabl
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