The board / graph theory / #546
Erdős Problem #546
PROVEDdatabase updated 2025-08-31
The statement as posed is true, and a proof exists.
What the community database records, not our verdict. erdosproblems.com no longer shows statuses (why).
Let \(G\) be a graph with no isolated vertices and \(m\) edges. Is it true that \[R(G) \leq 2^{O(m^{1/2})}?\] This is true, and was proved by Sudakov [Su11]. This problem is #11 in Ramsey Theory in the graphs problem collection.
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research solved. The authoritative wording is on erdosproblems.com/546.Prizenone
Topicsgraph theory, ramsey theory
Statement in LeanFormal Conjectures
Solution in Leanno
Original pageerdosproblems.com/546
Attempts
submit one →If you take a run at this one — with your own AI subscription or without — the guide says how, and the submission form gets you an honest read of what you found.