Piercing convex sets
نویسندگان
چکیده
منابع مشابه
Piercing convex sets and the Hadwiger Debrunner (p, q)-problem
A family of sets has the (p, q) property if among any p members of the family some q have a nonempty intersection. It is shown 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 . This settles an old problem of Hadwiger and Debr...
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In this paper, we study the number of compact sets needed in an infinite family of convex sets with a local intersection structure to imply a bound on its piercing number, answering a conjecture of Erdős and Grünbaum. Namely, if in an infinite family of convex sets in Rd we know that out of every p there are q which are intersecting, we determine if having some compact sets implies a bound on t...
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A finite collection C of closed convex sets in R is said to have a (p, q)-property if among any p members of C some q have a non-empty intersection, and |C| ≥ p. A piercing number of C is defined as the minimal number k such that there exists a k-element set which intersects every member of C. We focus on the simplest non-trivial case in R, i.e., p = 4 and q = 3. It is known that the maximum po...
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ژورنال
عنوان ژورنال: Bulletin of the American Mathematical Society
سال: 1992
ISSN: 0273-0979
DOI: 10.1090/s0273-0979-1992-00304-x