A Crossing Lemma for the Pair-Crossing Number

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, 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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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.Dept. Math., Physics, and Comp. Sci.University of Haifa at OranimTivonIsrael
  2. 2.School of ComputingDePaul UniversityChicagoUSA

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