On pseudo-disk hypergraphs

摘要

Let F be a family of pseudo-disks in the plane, and P be a finite subset of F. Consider the hyper-graph H(P, F) whose vertices are the pseudo-disks in Pand the edges are all subsets ofPof the form {D is an element of P vertical bar D boolean AND S not equal O}, where S is a pseudo-disk in F. We give an upper bound of O(nk(3)) for the number of edges inH(P, F) of cardinality at mostk. This generalizes a result of Buzaglo et al. [4].