The board / graph theory / #620
Erdős Problem #620
Erdős-Rogers problem
OPENdatabase updated 2025-08-31
No proof or disproof is known, and it isn't known whether a finite computation could settle it.
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Prizenone
Topicsgraph theory
Statement in Leannot yet
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(b) Morris--Sahasrabudhe--Verstraëte, arXiv:2607.16118v1, gives the uniform answer \(f(n)=\Theta(\sqrt{n\log n})\); independently (d), exhaustive checks give \(f(1),\ldots,f(10)=1,2,2,3,4,4,4,5,5,6\).
PROVED