منابع مشابه
Uniform Intersecting Families with Covering Number Restrictions
It is known that any k-uniform family with covering number t has at most k t t-covers. In this paper, we give better upper bounds for the number of t-covers in k-uniform intersecting families with covering number t.
متن کاملUniform Intersecting Families with Covering Number Four
Let X be a finite set. We denote by (~) the family of all k-element subsets of X. A family ~satisfying ~ c (~) is called k-uniform. The vertex set of @ is X and it is often denoted by V(Y). An element of ~ is also called an edge of J~. The family ~ is called intersecting if Fc~ G ¢ 25 holds for every F, G ~ ~ . A set C c X is called a cover (or transversal set) of Y if it intersects every edge ...
متن کاملCovers in 5-uniform intersecting families with covering number three
Let k be an integer. It is known that the maximum number of threecovers of a k-uniform intersecting family with covering number three is k − 3k + 6k − 4 for k = 3, 4 or k ≥ 9. In this paper, we prove that the same holds for k = 5, and show that a 5-uniform intersecting family with covering number three which has 76 three-covers is uniquely determined.
متن کاملCovering Intersecting Bi-set Families under Matroid Constraints
Edmonds’ fundamental theorem on arborescences [4] characterizes the existence of k pairwise edge-disjoint arborescences with the same root in a directed graph. In [9], Lovász gave an elegant alternative proof which became the base of many extensions of Edmonds’ result. In this paper, we use a modification of Lovász’ method to prove a theorem on covering intersecting bi-set families under matroi...
متن کامل- Covering Arrays and Intersecting Codes
A t-covering array is a set of k binary vectors of length n with the property that, in any t coordinate positions, all 2t possibilities occur at least once. Such arrays are used for example in circuit testing, and one wishes to minimize k for given values of n and t. The case t = 2 was solved by Rknyi, Katona, and Kleitman and Spencer. The present article is concerned with the case t = 3, where...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series A
سال: 2004
ISSN: 0097-3165
DOI: 10.1016/j.jcta.2004.05.005