Partial covering arrays and a generalized Erdös-Ko-Rado property
نویسندگان
چکیده
منابع مشابه
Partial Covering Arrays and a Generalized Erdős-Ko-Rado Property
The classical Erdős-Ko-Rado theorem states that if k ≤ ⌊n/2⌋ then the largest family of pairwise intersecting k-subsets of [n] = {0, 1, . . . , n} is of size ( n−1 k−1 ) . A family of k subsets satisfying this pairwise intersecting property is called an EKR family. We generalize the EKR property and provide asymptotic lower bounds on the size of the largest family A of k-subsets of [n] that sat...
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For a graph G, vertex v of G and integer r ≥ 1, we denote the family of independent r-sets of V (G) by I(r)(G) and the subfamily {A ∈ I(r)(G) : v ∈ A} by I v (G); such a subfamily is called a star. Then, G is said to be r-EKR if no intersecting subfamily of I(r)(G) is larger than the largest star in I(r)(G). If every intersecting subfamily of I v (G) of maximum size is a star, then G is said to...
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A k-uniform family of subsets of [n] is intersecting if it does not contain a disjoint pair of sets. The study of intersecting families is central to extremal set theory, dating back to the seminal Erdős–Ko–Rado theorem of 1961 that bounds the size of the largest such families. A recent trend has been to investigate the structure of set families with few disjoint pairs. Friedgut and Regev prove...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Designs
سال: 2010
ISSN: 1063-8539,1520-6610
DOI: 10.1002/jcd.20244