Bounding the piercing number

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Bounding the Piercing Number

It is shown that for every k and every p ≥ q ≥ d + 1 there is a c = c(k, p, q, d) < ∞ such that the following holds. For every family H whose members are unions of at most k compact, convex sets in R in which any set of p members of the family contains a subset of cardinality q with a nonempty intersection there is a set of at most c points in R that intersects each member of H. It is also show...

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ژورنال

عنوان ژورنال: Discrete & Computational Geometry

سال: 1995

ISSN: 0179-5376,1432-0444

DOI: 10.1007/bf02574042