Fractional Lengths and Crossing Numbers
Sýkora, Ondrej and Székely, László A. and Vrt'o, Imrich (2002) Fractional Lengths and Crossing Numbers. In: Graph Drawing 10th International Symposium, GD 2002, August 26-28, 2002, Irvine, CA, USA , pp. 186-192 (Official URL: http://dx.doi.org/10.1007/3-540-36151-0_18).
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Adamec and Nesetril  proposed a new the so called fractional length criterion for measuring the aesthetics of (artistic) drawings. They proposed to apply the criterion to the aesthetic drawing of graphs. In the graph drawing community, it is widely believed and even experimentally confirmed that the number of crossings is one of the most important aesthetic measures for nice drawings of graphs . The aim of this note is to demonstrate on two standard graph drawing models that in provably good drawings, with respect to the crossing number measure, the fractional length criterion is closely related to the crossing number criterion.
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