Geodesic
The number of crossings in a regular drawing of the complete bipartite graph
Journal of integer sequences, Tome 12 (2009) no. 5.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: The regular drawing of the complete bipartite graph $K_{n,n}$ produces a striking pattern comprising simple and multiple crossings. We compute the number $c(n)$ of crossings and give an asymptotic estimate for this sequence.
Classification : 05C62, 11A05
Keywords: complete bipartite graph, greatest common divisor 
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     author = {Legendre, St\'ephane},
     title = {The number of crossings in a regular drawing of the complete bipartite graph},
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Legendre, Stéphane. The number of crossings in a regular drawing of the complete bipartite graph. Journal of integer sequences, Tome 12 (2009) no. 5. http://geodesic.mathdoc.fr/item/JIS_2009__12_5_a2/