Discrete & Computational Geometry

, Volume 3, Issue 2, pp 97–102

Arrangements of lines with a minimum number of triangles are simple

  • Jean-Pierre Roudneff

DOI: 10.1007/BF02187900

Cite this article as:
Roudneff, J. Discrete Comput Geom (1988) 3: 97. doi:10.1007/BF02187900


Levi has shown that for every arrangement ofn lines in the real projective plane, there exist at leastn triangular faces, and Grünbaum has conjectured that equality can occur only for simple arrangements. In this note we prove this conjecture. The result does not hold for arrangements of pseudolines.

Copyright information

© Springer-Verlag New York Inc. 1988

Authors and Affiliations

  • Jean-Pierre Roudneff
    • 1
  1. 1.Université P. et M. CurieParisFrance