A Crossing Lemma for the pair-crossing number

Eyal Ackerman, Marcus Schaefer

Research output: Contribution to journalArticlepeer-review


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 pcr(G) ≥ c m3/n2. This bound is tight, up to the constant c. Here we show that c ≥ 1/34.2 if G is drawn without adjacent crossings.

Bibliographical note

Publisher Copyright:
© Springer-Verlag Berlin Heidelberg 2014.

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Computer Science


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