Erdős problem 61 · problems.science

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

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5 retained statements2415f78e850a

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FormalConjectures/ErdosProblems/

61.lean

Retained formal statement2 of 5

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

[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

1∀ {α : Type u_1} [inst : Fintype α] [inst_1 : DecidableEq α] (H : SimpleGraph α),2  ∃ c > 0, Erdos61.IsErdosHajnalLowerBound H fun n => Real.exp (c * √(Real.log ↑n * Real.log (Real.log ↑n)))

SolvedStatement only, no proof

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