Covering and packing for pairs
Abstract
When a v-set can be equipped with a set of k-subsets so that every 2-subset of the v-set appears in exactly (or at most, or at least) one of the chosen k-subsets, the result is a balanced incomplete block design (or packing, or covering, respectively). For each k, balanced incomplete block designs are known to exist for all sufficiently large values of v that meet certain divisibility conditions. When these conditions are not met, one can ask for the packing with the most blocks and/or the covering with the fewest blocks. Elementary necessary conditions furnish an upper bound on the number of blocks in a packing and a lower bound on the number of blocks in a covering. In this paper it is shown that for all sufficiently large values of v, a packing and a covering on v elements exist whose numbers of blocks differ from the basic bounds by no more than an additive constant depending only on k.
Additional Information
© 2013 Elsevier Inc. Received 24 September 2011. Available online 23 April 2013. We thank an anonymous referee for helpful comments on the presentation.Additional details
- Eprint ID
- 41568
- Resolver ID
- CaltechAUTHORS:20130930-153617380
- Created
-
2013-09-30Created from EPrint's datestamp field
- Updated
-
2021-11-10Created from EPrint's last_modified field