Resolvable coverings. (English) Zbl 0801.05020

Lamken, E. R.; Mills, W. H.

Congr. Numerantium 96, 21-26 (1993).

Summary: A minimum covering of pairs by triples in a \(6n\)-element set contains \(6n^ 2\) triples. Can such a covering be resolvable? A. Assaf, E. Mendelsohn and D. R. Stinson [Util. Math. 32, 67-74 (1987; Zbl 0649.05024)] showed that this is not possible for \(n<3\), and that for \(n\geq 3\) such a resolvable covering exists if \(n\not\in \{6,7,8,10,1,13,14,17,22\}\). In the present paper, we show that such resolvable coverings exist for these nine values of \(n\).

MSC:

05B40

Combinatorial aspects of packing and covering

Keywords:

triples; resolvable coverings