Hostname: page-component-78c5997874-8bhkd Total loading time: 0 Render date: 2024-11-16T07:28:04.778Z Has data issue: false hasContentIssue false
  • English
  • Français

Directed packings of pairs into quadruples

Part of: Designs and configurations

Published online by Cambridge University Press:  09 April 2009

David B. Skillicorn
David B. Skillicorn
Affiliation:
Department of Mathematics, Statistics and Computing ScienceDalhousie University Halifax, Nova Scotia B3H 4H8, Canada
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

A directed packing of pairs into quadruples is a collection of 4-subsets of a set of cardinality ν with the property that each ordered pair of elements appears at most once in a 4-subset (or block). The maximal number of blocks with this property is denoted by DD(2, 4, ν). Such a directed packing may also be thought of as a packing of transtivie tournaments into the complete directed graph on ν points. It is shown that, for all but a finite number of values of ν, DD(2, 4, ν) is maximal.

MSC classification

Secondary: 05B40: Packing and covering
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 33 , Issue 2 , October 1982 , pp. 179 - 184
Copyright
Copyright © Australian Mathematical Society 1982

References

[1]Brouwer, A. E., ‘Optimal packings of K4s into a Kn’, J. Combinatorial Theory B 26 (1979), 278–297.CrossRefGoogle Scholar
[2]Brouwer, A. E., Hanani, H. and Schrijver, A., ‘Group divisible designs with block size four’, Discrete Math. 20 (1977), 1–10.CrossRefGoogle Scholar
[3]Skillicorn, D. B., Directed packings and coverings with computer application (Ph.D. Thesis, University of Manitoba, 1981).Google Scholar
[4]Street, D. J. and Seberry, J. R., ‘All DBIBDs with block size four exist’, Utilitas Math. 17 (1980), 27–34.Google Scholar
[5]Wilson, R. M., ‘Construction and uses of pairwise balanced designs’, Proc. of NATO Advanced Study Inst. on Combinatorics, Nijenrode Castle, Brukelen (1974), pp. 19–42.Google Scholar