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Infinite Classes of Covering Numbers

Open Access article
 Printed: Dec 2000
  • I. Bluskov
  • M. Greig
  • K. Heinrich
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Let $D$ be a 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 number. In this paper we consider the case $t=2$, and find several infinite classes of covering numbers. We also give upper bounds on other classes of covering numbers.
MSC Classifications: 05B40, 05D05 show english descriptions Packing and covering [See also 11H31, 52C15, 52C17]
Extremal set theory
05B40 - Packing and covering [See also 11H31, 52C15, 52C17]
05D05 - Extremal set theory

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