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Equitable resolvable coverings
Author(s) -
van Dam Edwin R.,
Haemers Willem H.,
Peek Maurice B. M.
Publication year - 2003
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.10024
Subject(s) - combinatorics , mathematics , discrete mathematics
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