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Combinatorica

, Volume 17, Issue 1, pp 1–9 | Cite as

Quasi-planar graphs have a linear number of edges

  • Pankaj K. Agarwal
  • Boris Aronov
  • János Pach
  • Richard Pollack
  • Micha Sharir
Article

Abstract

A graph is calledquasi-planar if it can be drawn in the plane so that no three of its edges are pairwise crossing. It is shown that the maximum number of edges of a quasi-planar graph withn vertices isO(n).

Mathematics Subject Classification (1991)

05 C 35 05 C 40 68 R 05 

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Copyright information

© János Bolyai Mathematical Society 1997

Authors and Affiliations

  • Pankaj K. Agarwal
    • 1
  • Boris Aronov
    • 2
  • János Pach
    • 3
    • 4
    • 5
  • Richard Pollack
    • 4
  • Micha Sharir
    • 4
    • 6
  1. 1.Department of Computer ScienceDuke UniversityDurhamUSA
  2. 2.Computer and Information Science DepartmentPolytechnic UniversityBrooklynUSA
  3. 3.Department of Computer Science, City CollegeCUNYNew YorkUSA
  4. 4.Courant Institute of Mathematical SciencesNew York UniversityNew YorkUSA
  5. 5.Hungarian Academy of SciencesBudapestHungary
  6. 6.School of Mathematical SciencesTel Aviv UniversityTel AvivIsrael

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