𝔖 Bobbio Scriptorium
✦   LIBER   ✦

New upper bounds on the minimum size of covering designs

✍ Scribed by Iliya Bluskov; Heikki Hämäläinen

Publisher
John Wiley and Sons
Year
1998
Tongue
English
Weight
310 KB
Volume
6
Category
Article
ISSN
1063-8539

No coin nor oath required. For personal study only.

✦ Synopsis

Let D = {B1 , B2 , . . . , B b } be a finite family of k-subsets (called blocks) of a vset X(v) = {1, 2, . . . , v} (with elements called points). Then D is a (v, k, t) covering design or covering if every t-subset of X(v) is contained in at least one block of D. The number of blocks, b, is the size of the covering, and the minimum size of the covering is called the covering number, denoted C(v, k, t). This article is concerned with new constructions of coverings. The constructions improve many upper bounds on the covering number C(v, k, t)

📜 SIMILAR VOLUMES

General Upper Bounds on the Minimum Size
General Upper Bounds on the Minimum Size of Covering Designs
✍ Iliya Bluskov; Katherine Heinrich 📂 Article 📅 1999 🏛 Elsevier Science 🌐 English ⚖ 105 KB

Let D be a finite family of k-subsets (called blocks) of a v-set X(v). Then D is a (v, k, t) covering design or covering if every t-subset of X(v) is contained in at least one block of D. The number of blocks is the size of the covering, and the minimum size of the covering is called the covering nu

Upper Bounds on the Size of Obstructions
Upper Bounds on the Size of Obstructions and Intertwines
✍ Jens Lagergren 📂 Article 📅 1998 🏛 Elsevier Science 🌐 English ⚖ 417 KB

We give an exponential upper bound in p 4 on the size of any obstruction for path-width at most p. We give a doubly exponential upper bound in k 5 on the size of any obstruction for tree-width at most k. We also give an upper bound on the size of any intertwine of two given trees T and T $. The boun

New upper bounds on the decomposability
New upper bounds on the decomposability of planar graphs
✍ Fedor V. Fomin; Dimitrios M. Thilikos 📂 Article 📅 2005 🏛 John Wiley and Sons 🌐 English ⚖ 335 KB 👁 1 views

## Abstract It is known that a planar graph on __n__ vertices has branch‐width/tree‐width bounded by $\alpha \sqrt {n}$. In many algorithmic applications, it is useful to have a small bound on the constant α. We give a proof of the best, so far, upper bound for the constant α. In particular, for th

Upper Bounds on the Covering Radius of a
Upper Bounds on the Covering Radius of a Code with a Given Dual Distance
✍ S. Litsyn; A. Tietäväinen 📂 Article 📅 1996 🏛 Elsevier Science 🌐 English ⚖ 235 KB

We derive new upper bounds on the covering radius of a binary linear code as a function of its dual distance and dual-distance width . These bounds improve on the Delorme -Sole ´ -Stokes bounds , and in a certain interval for binary linear codes they are also better than Tieta ¨ va ¨ inen's bound .

An upper bound on the size of the larges
An upper bound on the size of the largest cliques in a graph
✍ Alain Billionnet 📂 Article 📅 1981 🏛 John Wiley and Sons 🌐 English ⚖ 194 KB 👁 1 views

## Abstract We produce in this paper an upper bound for the number of vertices existing in a clique of maximum cardinal. The proof is based in particular on the existence of a maximum cardinal clique that contains no vertex __x__ such that the neighborhood of __x__ is contained in the neighborhood