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Title: Packings of pairs with a minimum known number of quadruples (English)
Author: Novák, Jiří
Language: English
Journal: Mathematica Bohemica
ISSN: 0862-7959 (print)
ISSN: 2464-7136 (online)
Volume: 120
Issue: 4
Year: 1995
Pages: 367-377
Summary lang: English
Category: math
Summary: Let $E$ be an $n$-set. The problem of packing of pairs on $E$ with a minimum number of quadruples on $E$ is settled for $n<15$ and also for $n=36t+i$, $i=3$, $6$, $9$, $12$, where $t$ is any positive integer. In the other cases of $n$ methods have been presented for constructing the packings having a minimum known number of quadruples. (English)
Keyword: configuration
Keyword: packing of pairs
Keyword: quadruples
Keyword: packing of pairs with quadruples
Keyword: system of quadruples
Keyword: packing of $K_4$'s into $K_n$
MSC: 05B05
MSC: 05B40
idZBL: Zbl 0843.05017
idMR: MR1415084
DOI: 10.21136/MB.1995.126092
Date available: 2009-09-24T21:12:59Z
Last updated: 2020-07-29
Stable URL:
Reference: [1] A. E. Brouwer: Optimal packings of $K_4$'s into a $K_n$.J. Combinatorial Theory 26 (1979), 278-297. Zbl 0412.05030, MR 0535158, 10.1016/0097-3165(79)90105-5
Reference: [2] H. Hanani: The existence and construction of balanced incomplete block design.Ann. Math. Statist. 32 (1961), 361-386. MR 0166888, 10.1214/aoms/1177705047
Reference: [3] J. Novák: Edge-bases of complete uniform hypergraphs.Mat. čas. 24 (1974), 43-57. MR 0357242
Reference: [4] C. Colbourn A. Rosa Š. Znám: The spectrum of maximal partial Steiner triple systems.Math. Reports Mc. Master University. 1991.
Reference: [5] P. Turán: On the theory of graphs.Colloq. Math. 3 (1955), 19-30. MR 0062416


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