منابع مشابه
Random Covering Designs
A t (n; k; ) covering design (n k > t 2) consists of a collection of k-element subsets (blocks) of an n-element set X such that each t-element subset of X occurs in at least blocks. Let = 1 and k 2t 1. Consider a randomly selected collection B of blocks; jBj = (n). We use the correlation inequalities of Janson ([10], [1]) to show that B exhibits a rather sharp threshold behaviour, in the sense ...
متن کاملAsymptotically Optimal Covering Designs
A (v, k, t) covering design, or covering, is a family of k-subsets, called blocks, chosen from a v-set, such that each t-subset is contained in at least one of the blocks. The number of blocks is the covering’s size, and the minimum size of such a covering is denoted by C(v, k, t). It is easy to see that a covering must contain at least (v t )
متن کاملSteiner pentagon covering designs
Let Kn denote the complete undirected graph on n vertices. A Steiner pentagon covering design (SPCD) of order n is a pair (Kn;B), where B is a collection of c(n)= n=5 n−1=2 pentagons from Kn such that any two vertices are joined by a path of length 1 in at least one pentagon of B, and also by a path of length 2 in at least one pentagon of B. The existence of SPCDs is investigated. The main appr...
متن کاملSingle-change circular covering designs
A single-change circular covering design (scccd) based on the set [v] = { 1 . . . . . t:} with block size k is an ordered collection o f b blocks, ~ = {Bi . . . . . B/,}, each B~ C [v], which obey: ( 1 ) each block differs from the previous block by a single element, as does the last from the first, and, (2) every pair of [v] is covered by some block. The object is to minimize b for a fixed v a...
متن کاملNew Constructions for Covering Designs
A (v, k, t) covering design, or covering, is a family of k-subsets, called blocks, chosen from a v-set, such that each t-subset is contained in at least one of the blocks. The number of blocks is the covering’s size, and the minimum size of such a covering is denoted by C(v, k, t). This paper gives three new methods for constructing good coverings: a greedy algorithm similar to Conway and Sloan...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series A
سال: 1996
ISSN: 0097-3165
DOI: 10.1006/jcta.1996.0065