Equitable resolvable coverings

✍ Scribed by Edwin R. van Dam; Willem H. Haemers; Maurice B. M. Peek

• Publisher: John Wiley and Sons
• Year: 2003
• Tongue: English
• Weight: 116 KB
• Volume: 11
• Category: Article
• ISSN: 1063-8539
• DOI: 10.1002/jcd.10024

✦ Synopsis

Abstract

In an earlier article, Willem H. Haemers has determined the minimum number of parallel classes in a resolvable 2‐(qk,k,1) covering for all k ≥ 2 and q = 2 or 3. Here, we complete the case q = 4, by construction of the desired coverings using the method of simulated annealing. Secondly, we look at equitable resolvable 2‐(qk,k,1) coverings. These are resolvable coverings which have the additional property that every pair of points is covered at most twice. We show that these coverings satisfy k < 2q −  $\sqrt{2q - {9\over4}}$, and we give several examples. In one of these examples, k > q. © 2003 Wiley Periodicals, Inc. J Combin Designs 11: 113–123, 2003; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/jcd.10024