Cookies

We use cookies to ensure that we give you the best experience on our website. By continuing to browse this repository, you give consent for essential cookies to be used. You can read more about our Privacy and Cookie Policy.


Durham Research Online
You are in:

Enclosings of decompositions of complete multigraphs in 2-factorizations.

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
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

Save or Share this output

Export:
Export
Look up in GoogleScholar