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Arrangements of Pseudocircles: Triangles and Drawings
[article]

2020
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arXiv
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pre-print

A pseudocircle is a simple closed curve on the sphere or in the plane. The study of arrangements of pseudocircles was initiated by Grünbaum, who defined them as collections of simple closed curves that pairwise intersect in exactly two crossings. Grünbaum conjectured that the number of triangular cells p_3 in digon-free arrangements of n pairwise intersecting pseudocircles is at least 2n-4. We present examples to disprove this conjecture. With a recursive construction based on an example with

arXiv:1708.06449v4
fatcat:lbmt6rapwnht7eh4u6ckygjysi