Consider the hypergraph whose vertex set is a family of n lines in general position in the plane, and whose hyperedges are induced by intersections with a finite family of pseudo-discs. We prove that the number of 3-sized hyperedges is bounded by O  (n^2) and that this bound is tight. In addition, we show that the total number of hyperedges is  O(n^3)  .
Consider the hypergraph whose vertex set is a family of n lines in general position in the plane, and whose hyperedges are induced by intersections with a family of pseudo-discs. We prove that the number of t-hyperedges is bounded by O _t (n^2) and that the total number of hyperedges is bounded by O(n^3) . Both bounds are tight .
D
finite
R
3-sized hyperedges
t-hyperedges
A
_t
D
this bound is tight. In addition, we show that
A
bounded by
A
. Both bounds are tight