منابع مشابه
Maximum union-free subfamilies
An old problem of Moser asks: what is the size of the largest union-free subfamily that one can guarantee in every family of m sets? A family of sets is called union-free if there are no three distinct sets in the family such that the union of two of the sets is equal to the third set. We show that every family of m sets contains a union-free subfamily of size at least √4m + 1 − 1 and that this...
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Frankl and F uredi established that the largest number of 3-subsets of an n-set for which no four distinct sets A; B; C; D satisfy A B = C D is at most b n(n?1) 3 c. Chee, Colbourn, and Ling established that this upper bound is met, with few exceptions, when n 0; 1 (mod 3). In this paper, it is established that the upper bound is also met with few exceptions when n 2 (mod 3).
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Asteroidal triple free (AT-free) graphs have been introduced as a generalization of interval graphs, since interval graphs are exactly the chordal AT-free graphs. While for interval graphs it is obvious that there is always a linear ordering of the vertices, such that for each triple of independent vertices the middle one intercepts any path between the remaining vertices of the triple, it is n...
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In this paper, we settle a problem of Frankl and Filredi, which is a special case of a problem of Erdt~s, determining the maximum number of hyperedges in a 3-uniform hypergraph in which no two pairs of distinct hyperedges have the same union. The extremal case corresponds to the existence of weakly union-free twofold triple systems, which is settled here with six definite and four possible exce...
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ژورنال
عنوان ژورنال: Israel Journal of Mathematics
سال: 2012
ISSN: 0021-2172,1565-8511
DOI: 10.1007/s11856-012-0017-0