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Enclosings of decompositions of complete multigraphs in 2-factorizations

Feghali, Carl; Johnson, Matthew

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Authors

Carl Feghali



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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