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Kirkman packing and covering designs with spanned holes of size 2

✍ Scribed by Jianxing Yin

Publisher: John Wiley and Sons
Year: 2005
Tongue: English
Weight: 120 KB
Volume: 13
Category: Article
ISSN: 1063-8539
DOI: 10.1002/jcd.20034

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✦ Synopsis

Abstract

A Kirkman holey packing (resp. covering) design, denoted by KHPD(g^u^) (resp. KHCD(g^u^)), is a resolvable (gu, 3, 1) packing (resp. covering) design of pairs with u disjoint holes of size g, which has the maximum (resp. minimum) possible number of parallel classes. Each parallel class contains one block of size δ, while other blocks have size 3. Here δ is equal to 2, 3, and 4 when gu ≡ 2, 3, and 4 (mod 3) in turn. In this paper, the existence problem of a KHPD(2^u^) and a KHCD(2^u^) is solved with one possible exception of a KHPD(2^8^). © 2004 Wiley Periodicals, Inc.

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