Journal of Integer Sequences, Vol. 12 (2009), Article 09.5.5

The Number of Crossings in a Regular Drawing of the Complete Bipartite Graph

Stéphane Legendre
Team of Mathematical Eco-Evolution
Ecole Normale Supérieure
75005 Paris


The regular drawing of the complete bipartite graph Kn,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.

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(Concerned with sequences A000537 A115004 A159065.)

Received April 20 2009; revised version received July 10 2009. Published in Journal of Integer Sequences, July 10 2009.

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