Article

Combinatorica

, Volume 17, Issue 1, pp 1-9

First online:

Quasi-planar graphs have a linear number of edges

  • Pankaj K. AgarwalAffiliated withDepartment of Computer Science, Duke University
  • , Boris AronovAffiliated withComputer and Information Science Department, Polytechnic University
  • , János PachAffiliated withDepartment of Computer Science, City College, CUNYCourant Institute of Mathematical Sciences, New York UniversityHungarian Academy of Sciences
  • , Richard PollackAffiliated withCourant Institute of Mathematical Sciences, New York University
  • , Micha SharirAffiliated withCourant Institute of Mathematical Sciences, New York UniversitySchool of Mathematical Sciences, Tel Aviv University

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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