Abstract
It
and
are two families of pairwise disjoint simple closed curves in the plane such that each curve in
intersects each curve in
, then the total number of points of intersection in
is at least 2(m−1)n, where
, and this bound is best possible. We use this to show that the cartesian product of two 5-cycles has crossing number 15.
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Richter, R.B., Thomassen, C. Intersections of curve systems and the crossing number ofC 5 ×C 5 . Discrete Comput Geom 13, 149–159 (1995). https://doi.org/10.1007/BF02574034
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DOI: https://doi.org/10.1007/BF02574034