Covering and packing for pairs

Yeow Meng Chee, Charles Colbourn, Alan C H Ling, Richard M. Wilson

Research output: Contribution to journalArticle

11 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)1440-1449
Number of pages10
JournalJournal of Combinatorial Theory. Series A
Volume120
Issue number7
DOIs
StatePublished - Sep 1 2013

Keywords

  • Balanced incomplete block design
  • Group divisible design
  • Pair covering
  • Pair packing
  • Pairwise balanced design

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics

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