Carl Feghali
Enclosings of decompositions of complete multigraphs in 2-factorizations
Feghali, Carl; Johnson, Matthew
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.
Citation
Feghali, C., & Johnson, M. (2018). Enclosings of decompositions of complete multigraphs in 2-factorizations. Journal of Combinatorial Designs, 26(5), 205-218. https://doi.org/10.1002/jcd.21601
Journal Article Type | Article |
---|---|
Acceptance Date | Jan 1, 2018 |
Online Publication Date | Jan 18, 2018 |
Publication Date | May 1, 2018 |
Deposit Date | Mar 15, 2018 |
Publicly Available Date | Mar 29, 2024 |
Journal | Journal of Combinatorial Designs |
Print ISSN | 1063-8539 |
Electronic ISSN | 1520-6610 |
Publisher | Wiley |
Peer Reviewed | Peer Reviewed |
Volume | 26 |
Issue | 5 |
Pages | 205-218 |
DOI | https://doi.org/10.1002/jcd.21601 |
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Copyright 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.
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