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Resolvable packings of K v with K 2 × K c 's
Author(s) -
Li Yang,
Yin Jianxing
Publication year - 2009
Publication title -
journal of combinatorial designs
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.618
H-Index - 34
eISSN - 1520-6610
pISSN - 1063-8539
DOI - 10.1002/jcd.20197
Subject(s) - combinatorics , mathematics , upper and lower bounds , discrete mathematics , mathematical analysis
Abstract The study of resolvable packings of K v with K r × K c 's is motivated by the use of DNA library screening. We call such a packing a ( v , K r × K c , 1)‐RP. As usual, a ( v , K r × K c , 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 , K r × K c , 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, K 2 × K c , 1)‐RPs meeting the aforementioned bound and establish some existence results. In particular, we show that an optimal ( v, K 2 × K 3 , 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