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A Crossing Lemma for the Pair-Crossing Number

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Part of the Lecture Notes in Computer Science book series (LNTCS,volume 8871)


The pair-crossing 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 \({\mbox{pcr}}(G) \geq c \frac{m^3}{n^2}\). 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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Ackerman, E., Schaefer, M. (2014). A Crossing Lemma for the Pair-Crossing Number. In: Duncan, C., Symvonis, A. (eds) Graph Drawing. GD 2014. Lecture Notes in Computer Science, vol 8871. Springer, Berlin, Heidelberg.

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  • Print ISBN: 978-3-662-45802-0

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