Publication details for Professor Matthew JohnsonFeghali, Carl & Johnson, Matthew (2018). Enclosings of decompositions of complete multigraphs in 2-factorizations. Journal of Combinatorial Designs 26(5): 205-218.
- Publication type: Journal Article
- ISSN/ISBN: 1063-8539 (print), 1520-6610
- DOI: 10.1002/jcd.21601
- Further publication details on publisher web site
- Durham Research Online (DRO) - may include full text
Author(s) from Durham
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.