Minimal paths and cycles in set systems
نویسندگان
چکیده
منابع مشابه
Minimal paths and cycles in set systems
A minimal k-cycle is a family of sets A0, . . . , Ak−1 for which Ai ∩Aj 6= ∅ if and only if i = j or i and j are consecutive modulo k. Let fr(n, k) be the maximum size of a family of r-sets of an n element set containing no minimal k-cycle. Our results imply that for fixed r, k ≥ 3, ` ( n− 1 r − 1 ) +O(nr−2) ≤ fr(n, k) ≤ 3` ( n− 1 r − 1 ) +O(nr−2), where ` = b(k− 1)/2c. We also prove that fr(n,...
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ژورنال
عنوان ژورنال: European Journal of Combinatorics
سال: 2007
ISSN: 0195-6698
DOI: 10.1016/j.ejc.2006.07.001