The board / graph theory / #800
Erdős Problem #800
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).
If \(G\) is a graph on \(n\) vertices which has no two adjacent vertices of degree \(\geq 3\) then \[R(G)\ll n,\] where the implied constant is absolute. A problem of Burr and Erdős. Solved in the affirmative by Alon [Al94].
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research solved. The authoritative wording is on erdosproblems.com/800.Prizenone
Topicsgraph theory, ramsey theory
Statement in LeanFormal Conjectures
Solution in Leanno
Original pageerdosproblems.com/800
Attempts
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