Configurations in 4-cycle systems

Bryant, D, Grannell, M, Griggs, T and Macaj, M (2004) Configurations in 4-cycle systems. Graphs And Combinatorics, 20 2: 161-179. doi:10.1007/s00373-004-0553-4


Author Bryant, D
Grannell, M
Griggs, T
Macaj, M
Title Configurations in 4-cycle systems
Journal name Graphs And Combinatorics   Check publisher's open access policy
ISSN 0911-0119
Publication date 2004-01-01
Sub-type Article (original research)
DOI 10.1007/s00373-004-0553-4
Volume 20
Issue 2
Start page 161
End page 179
Total pages 19
Editor J. Akiyama
M. Kano
Place of publication Japan
Publisher Springer-Verlag
Language eng
Subject C1
230101 Mathematical Logic, Set Theory, Lattices And Combinatorics
780101 Mathematical sciences
Abstract A 4-cycle system of order n, denoted by 4CS(n), exists if and only if nequivalent to1 (mod 8). There are four configurations which can be formed by two 4-cycles in a 4CS(n). Formulas connecting the number of occurrences of each such configuration in a 4CS(n) are given. The number of occurrences of each configuration is determined completely by the number d of occurrences of the configuration D consisting of two 4-cycles sharing a common diagonal. It is shown that for every nequivalent to1 (mod 8) there exists a 4CS(n) which avoids the configuration D, i.e. for which d=0. The exact upper bound for d in a 4CS(n) is also determined.
Keyword Mathematics
4-cycle System
Configurations
Avoidance
Steiner Triple-systems
Q-Index Code C1

 
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Created: Wed, 15 Aug 2007, 13:05:06 EST