Abstract
AbstractThe study of resolvable packings of Kv with Kr × Kc's is motivated by the use of DNA library screening. We call such a packing a (v, Kr × Kc, 1)‐RP. As usual, a (v, Kr × Kc, 1)‐RP with the largest possible number of parallel classes (or, equivalently, the largest possible number of blocks) is called optimal. The resolvability implies v ≡ 0 (mod rc). Let ρ be the number of parallel classes of a (v, Kr × Kc, 1)‐RP. Then we have ρ ≤ ⌊(v‐1)/(r + c − 2)⌋. In this article, we present a number of constructive methods to obtain optimal (v, K2 × Kc, 1)‐RPs meeting the aforementioned bound and establish some existence results. In particular, we show that an optimal (v, K2 × K3, 1)‐RP meeting the bound exists if and only if v ≡ 0 (mod 6). © 2008 Wiley Periodicals, Inc. J Combin Designs 17: 177–189, 2009
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