International Symposium on Graph Drawing

GD 2014: Graph Drawing pp 222-233

A Crossing Lemma for the Pair-Crossing Number

  • Eyal Ackerman
  • Marcus Schaefer
Conference paper

DOI: 10.1007/978-3-662-45803-7_19

Volume 8871 of the book series Lecture Notes in Computer Science (LNCS)
Cite this paper as:
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

Abstract

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

  • Eyal Ackerman
    • 1
  • Marcus Schaefer
    • 2
  1. 1.Dept. Math., Physics, and Comp. Sci.University of Haifa at OranimTivonIsrael
  2. 2.School of ComputingDePaul UniversityChicagoUSA