On lower bound.

It has been shown that $ \lim_{n\rightarrow\infty}\frac{cr(K_n)}{Z(n)}\geq 0.83 $, where $ Z(n) $ is the conjectured value. For the proof, see de Klerk, E.; Maharry, J.; Pasechnik, D. V.; Richter, R. B.; Salazar, G. Improved bounds for the crossing numbers of $ K\sb {m,n} $ and $ K\sb n $. (2007).


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