Intersection Properties of Families Containing Sets of Nearly the Same Size
نویسندگان
چکیده
A family F of sets has property B(s) if there exists a set S whose intersection with each set in F is non-empty but contains fewer than s elements . P . Erdős has asked whether there exists an absolute constant c such that every projective plane has property B(c) . In this paper, the authors, as a partial answer to this question, obtain the result that for n sufficiently large, every projective plane of order n has property B(c log n) . The result is a corollary of a theorem applicable to somewhat more general families of finite sets .
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