Discrete & Computational Geometry

, Volume 3, Issue 1, pp 97-102

Arrangements of lines with a minimum number of triangles are simple

  • Jean-Pierre RoudneffAffiliated withUniversité P. et M. Curie

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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.