A Crossing Lemma for the PairCrossing NumberAckerman, Eyal and Schaefer, Marcus (2014) A Crossing Lemma for the PairCrossing Number. In: Graph Drawing 22nd International Symposium, GD 2014, September 2426, 2014 , pp. 222233(Official URL: http://dx.doi.org/10.1007/9783662458037_19). Full text not available from this repository.
Official URL: http://dx.doi.org/10.1007/9783662458037_19
AbstractThe paircrossing number of a graph G, pcr(G), is the minimum possible number of pairs of edges that cross each other (possibly several times) in a drawing of G. It is known that there is a constant c ≥ 1/64 such that for every (not too sparse) graph G with n vertices and m edges pcr(G)≥c(m^3/n^2) . This bound is tight, up to the constant c. Here we show that c ≥ 1/34.2 if G is drawn without adjacent crossings.
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