## Complete sets of metamorphoses: Twofold 4-cycle systems into twofold 6-cycle systems

dc.contributor.author | Billington, Elizabeth J. | |

dc.contributor.author | Cavenagh, Nicholas J. | |

dc.contributor.author | Khodkar, Abdollah | |

dc.date.accessioned | 2013-02-17T20:53:10Z | |

dc.date.available | 2013-02-17T20:53:10Z | |

dc.date.copyright | 2012-08 | |

dc.date.issued | 2012 | |

dc.identifier.citation | Billington, E. J., Cavenagh, N. J., & Khodkar, A. (2012). Complete sets of metamorphoses: Twofold 4-cycle systems into twofold 6-cycle systems. Discrete Mathematics, 312(16), 2438-2445. | en_NZ |

dc.identifier.issn | 0012-365X | |

dc.identifier.uri | https://hdl.handle.net/10289/7208 | |

dc.description.abstract | Let (X,C) denote a twofold k-cycle system with an even number of cycles. If these k-cycles can be paired together so that: (i) each pair contains a common edge; (ii) removal of the repeated common edge from each pair leaves a (2k-2)-cycle; (iii) all the repeated edges, once removed, can be rearranged exactly into a collection of further (2k-2)-cycles; then this is a metamorphosis of a twofold k-cycle system into a twofold (2k-2)-cycle system. The existence of such metamorphoses has been dealt with for the case of 3-cycles (Gionfriddo and Lindner, 2003) [3] and 4-cycles (Yazc, 2005) [7]. If a twofold k-cycle system (X,C) of order n exists, which has not just one but has k different metamorphoses, from k different pairings of its cycles, into twofold (2k-2)-cycle systems, such that the collection of all removed double edges from all k metamorphoses precisely covers 2 Kn, we call this a complete set of twofold paired k-cycle metamorphoses into twofold (2k-2)-cycle systems. In this paper, we show that there exists a twofold 4-cycle system (X,C) of order n with a complete set of metamorphoses into twofold 6-cycle systems if and only if n≡0,1,9,16 (mod 24), n≠9. | en_NZ |

dc.language.iso | en | |

dc.publisher | Elsevier | en_NZ |

dc.relation.ispartof | Discrete Mathematics | |

dc.subject | Cycle decomposition | en_NZ |

dc.subject | Metamorphosis | en_NZ |

dc.subject | Twofold cycle system | en_NZ |

dc.title | Complete sets of metamorphoses: Twofold 4-cycle systems into twofold 6-cycle systems | en_NZ |

dc.type | Journal Article | en_NZ |

dc.identifier.doi | 10.1016/j.disc.2012.04.029 | en_NZ |

dc.relation.isPartOf | Discrete Mathematics | en_NZ |

pubs.begin-page | 2438 | en_NZ |

pubs.elements-id | 38214 | |

pubs.end-page | 2445 | en_NZ |

pubs.issue | 16 | en_NZ |

pubs.volume | 312 | en_NZ |

uow.identifier.article-no | 16 | en_NZ |

## Files in this item

Files | Size | Format | View |
---|---|---|---|

There are no files associated with this item. |