Abstract
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.
Article PDF
Similar content being viewed by others
References
B. Grünbaum,Arrangements and Spreads, Regional Conference Series in Mathematics 10, American Mathematical Society, Providence, RI, 1972.
F. Levi, Die Teilung der projektiven Ebene durch Gerade oder Pseudogerade,Ber. Math.-Phys. Kl. Sächs. Akad. Wiss. Leipzig 78 (1926), 256–267
J.-P. Roudneff, The maximum number of triangles in arrangements of (pseudo)-lines, submitted.
J.-P. Roudneff, Quadrilaterals and pentagons in arrangements of lines,Geom. Dedicata, to appear.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Roudneff, JP. Arrangements of lines with a minimum number of triangles are simple. Discrete Comput Geom 3, 97–102 (1988). https://doi.org/10.1007/BF02187900
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/BF02187900