A Purely Combinatorial Proof of the Hadwiger Debrunner
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چکیده
A family of sets has the (p; q) property if among any p members of the family some q have a nonempty intersection. The authors have proved that for every p q d + 1 there is a c = c(p; q; d) < 1 such that for every family F of compact, convex sets in R d which has the (p; q) property there is a set of at most c points in R d that intersects each member of F, thus settling an old problem of Hadwiger and Debrunner. Here we present a purely combinatorial proof of this result.
منابع مشابه
A purely combinatorial proof of the Hadwiger Debrunner (p, q) Conjecture
Abstract A family of sets has the (p, q) property if among any p members of the family some q have a nonempty intersection. The authors have proved that for every p ≥ q ≥ d+ 1 there is a c = c(p, q, d) < ∞ such that for every family F of compact, convex sets in R which has the (p, q) property there is a set of at most c points in R that intersects each member of F , thus settling an old problem...
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تاریخ انتشار 1997