Percentages in Pairwise Balanced Designs

Charles J. Colbourn, Vojtech Rötdl

Research output: Contribution to journalArticlepeer-review


Let K ={K1,…, km} be a set of block sizes, and let {p1,…, pm} be nonnegative numbers with Σmi=1, pi We prove the following theorem: for any ε>0, if a (v, K, 1) pairwise balanced design exists and v is sufficiently large, then a (v, K, 1) pairwise balanced design exists in which the fraction of pairs appearing in blocks of size kiis pi,±ε for every i. We also show that the necessary conditions for a pairwise balanced design having precisely the fraction pi, of its pairs in blocks of size ki for each i are asymptotically sufficient.

Original languageEnglish (US)
Pages (from-to)57-63
Number of pages7
JournalAnnals of Discrete Mathematics
Issue numberC
StatePublished - Jan 1 1989
Externally publishedYes

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics


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