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On s-intersecting curves and related problems

2008
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Proceedings of the twenty-fourth annual symposium on Computational geometry - SCG '08
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Let P be a set of n points in the plane and let C be a family of simple closed curves in the plane each of which avoids the points of P . For every curve C ∈ C we denote by disc(C) the region in the plane bounded by C. Fix an integer k ≥ 0 and assume that every two curves in C intersect at most k times and that for every two curves C, C ′ ∈ C the intersection disc(C) ∩ disc(C ′ ) is a connected set. We consider the family F = {P ∩ disc(C) | C ∈ C}. When k is even, we provide sharp bounds, in

doi:10.1145/1377676.1377690
dblp:conf/compgeom/BuzagloHP08
fatcat:umhfi4fom5frvmu2o3yvvgn3mi