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On the number of intersections of two polygons

Jakub Černý;  Jan Kára;  Daniel Kráľ;  Pavel Podbrdský;  Miroslava Sotáková;  Robert Šámal — 2003

Commentationes Mathematicae Universitatis Carolinae

We study the maximum possible number f ( k , l ) of intersections of the boundaries of a simple k -gon with a simple l -gon in the plane for k , l ≥ 3 . To determine the number f ( k , l ) is quite easy and known when k or l is even but still remains open for k and l both odd. We improve (for k ≤ l ) the easy upper bound k l - l to k l - k / 6 - l and obtain exact bounds for k = 5 ( f ( 5 , l ) = 4 l - 2 ) in this case.

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