Bryant, Darryn; Grannell, Mike; Griggs, Terry and Macaj, Martin
(2004).
*Graphs and Combinatorics*, 20(2) pp. 161–179.

URL: | http://search.epnet.com./login.aspx?direct=true&db... |
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DOI (Digital Object Identifier) Link: | https://doi.org/10.1007/s00373-004-0553-4 |

Google Scholar: | Look up in Google Scholar |

## 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 Item |
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ISSN: | 1435-5914 |

Extra Information: | 4-cycle system; Configurations; Avoidance; Algebra; Combinatorial analysis; Decomposition (Mathematics); Graph theory; Mathematics; Bipartite graphs |

Academic Unit/School: | Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics Faculty of Science, Technology, Engineering and Mathematics (STEM) |

Item ID: | 2149 |

Depositing User: | Mike Grannell |

Date Deposited: | 06 Jun 2006 |

Last Modified: | 07 Dec 2018 08:51 |

URI: | http://oro.open.ac.uk/id/eprint/2149 |

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