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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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The source's own material, retained exactly.

5 retained statements36c6d0fef71a

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FormalConjectures/ErdosProblems/

61.lean

Retained formal statement2 of 5

Bucić, Nguyen, Scott, and Seymour [BNSS23] improved this to f(n)=exp⁡(cHlog⁡nlog⁡log⁡n)f(n) = \exp(c_H \sqrt{\log n \log \log n}) for some constant cH>0c_H > 0 depending on HH.

[BNSS23] Bucić, M. and Nguyen, T. and Scott, A. and Seymour, P., A loglog step towards Erdos-Hajnal

FormalConjectures/ErdosProblems/61.leanErdos61.erdos_61.variants.bnss232 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 * Real.log (Real.log ↑n)))
SolvedStatement only, no proof