Feghali, Carl and Johnson, Matthew (2018) 'Enclosings of decompositions of complete multigraphs in 2-factorizations.', *Journal of combinatorial designs.*, 26 (5). pp. 205-218.

## Abstract

Let k, m, n, λ, and μ be positive integers. A decomposition of math formula into edge-disjoint subgraphs math formula is said to be enclosed by a decomposition of math formula into edge-disjoint subgraphs math formula if math formula and, after a suitable labeling of the vertices in both graphs, math formula is a subgraph of math formula and math formula is a subgraph of math formula for all math formula. In this paper, we continue the study of enclosings of given decompositions by decompositions that consist of spanning subgraphs. A decomposition of a graph is a 2-factorization if each subgraph is 2-regular and spanning, and is Hamiltonian if each subgraph is a Hamiltonian cycle. We give necessary and sufficient conditions for the existence of a 2-factorization of math formula that encloses a given decomposition of math formula whenever math formula and math formula. We also give necessary and sufficient conditions for the existence of a Hamiltonian decomposition of math formula that encloses a given decomposition of math formula whenever math formula and either math formula or math formula and math formula, or math formula, math formula, and math formula.

Item Type: | Article |
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Full text: | (AM) Accepted Manuscript Download PDF (185Kb) |

Status: | Peer-reviewed |

Publisher Web site: | https://doi.org/10.1002/jcd.21601 |

Publisher statement: | This is the accepted version of the following article: Feghali C, Johnson M. (2018) Enclosings of decompositions of complete multigraphs in 2-factorizations. Journal of Combinatorial Designs, 26(5): 205-218, which has been published in final form at https://doi.org/10.1002/jcd.21601. This article may be used for non-commercial purposes in accordance With Wiley Terms and Conditions for self-archiving. |

Date accepted: | 01 January 2018 |

Date deposited: | 16 March 2018 |

Date of first online publication: | 18 January 2018 |

Date first made open access: | 18 January 2019 |

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