Drawing K_{2,n}: A Lower Bound. T. Biedl, T. Chan, A. López-Ortiz. In Proceedings of Canadian Conference on Computational Geometry, 2002. PostScript file.

Abstract. We give a tradeoff theorem between the area and the aspect ratio required by any planar straight-line drawing of K_{2,n} on the integer lattice. In particular we show that if the drawing is contained in a rectangle of area O(n) then the rectangle must have

aspect ratio Omega(n), and conversely, if the aspect ratio is 1 then the area must be Omega(n^2/log^2 n).