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Erdős problem 61

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The Erdős–Hajnal Conjecture states that there is a constant c(H)>0c(H) > 0 for each HH such that we can take f(n)=nc(H)f(n) = n^{c(H)} in the above formulation.

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FormalConjectures/ErdosProblems/

61.lean

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Erdős and Hajnal [ErHa89] proved that we can take f(n)=exp⁡(cHlog⁡n)f(n) = \exp(c_H \sqrt{\log n}) for some constant cH>0c_H > 0 depending on HH.

[ErHa89] Erdős, P. and Hajnal, A., Ramsey-type theorems. Discrete Appl. Math. (1989), 37-52.

FormalConjectures/ErdosProblems/61.leanErdos61.erdos_61.variants.erha892 linesExact file
∀ {α : Type u_1} [inst : Fintype α] [inst_1 : DecidableEq α] (H : SimpleGraph α),  ∃ c > 0, Erdos61.IsErdosHajnalLowerBound H fun n => Real.exp (c * √(Real.log ↑n))
SolvedStatement only, no proof