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Durham University

Computer Science

Profile

Publication details for Professor Matthew Johnson

Feghali, Carl & Johnson, Matthew (2018). Enclosings of decompositions of complete multigraphs in 2-factorizations. Journal of Combinatorial Designs 26(5): 205-218.

Author(s) from Durham

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.