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.

Sources

Browse retained paths and inspect the exact material available for this Problem.

5 retained statements2415f78e850a

Open selected source

FormalConjectures/ErdosProblems/

61.lean

Retained formal statement4 of 5

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

[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

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))

SolvedStatement only, no proof

Sources

Search problems.science