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Configurations in 4-cycle systems

Bryant, Darryn; Grannell, Mike; Griggs, Terry and Macaj, Martin (2004). Configurations in 4-cycle systems. Graphs and Combinatorics, 20(2) pp. 161–179.

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DOI (Digital Object Identifier) Link: http://dx.doi.org/10.1007/s00373-004-0553-4
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Abstract

A 4-cycle system of order n, denoted by 4CS(n), exists if and only if n=1 (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 n=1 (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.

Item Type: Journal Article
ISSN: 1435-5914
Extra Information: 4-cycle system; Configurations; Avoidance; Algebra; Combinatorial analysis; Decomposition (Mathematics); Graph theory; Mathematics; Bipartite graphs
Academic Unit/Department: Mathematics, Computing and Technology > Mathematics and Statistics
Item ID: 2149
Depositing User: Mike Grannell
Date Deposited: 06 Jun 2006
Last Modified: 02 Dec 2010 19:46
URI: http://oro.open.ac.uk/id/eprint/2149
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