The Hamilton-Waterloo Problem with 4-Cycles and a Single Factor of n-Cycles
Document Type
Article
Publication Date
11-2013
Department
Department of Mathematical Sciences
Abstract
A 2-factor in a graph G is a 2-regular spanning subgraph of G, and a 2-factorization of G is a decomposition of all the edges of G into edge-disjoint 2-factors. A {Cmr, Cns}-factorization of Kυasks for a 2-factorization of Kυ, where r of the 2-factors consists of m-cycles, and s of the 2-factors consists of n-cycles. This is a case of the Hamilton-Waterloo problem with uniform cycle sizes m and n. If υ is even, then it is a decomposition of Kυ- F where a 1-factor F is removed from Kυ. We present necessary and sufficient conditions for the existence of a {C4r, Cn1}-factorization of Kυ- F.
Publication Title
Graphs and Combinatorics
Recommended Citation
Keranen, M. S.,
&
Özkan, S.
(2013).
The Hamilton-Waterloo Problem with 4-Cycles and a Single Factor of n-Cycles.
Graphs and Combinatorics,
29(6), 1827-1837.
http://doi.org/10.1007/s00373-012-1231-6
Retrieved from: https://digitalcommons.mtu.edu/michigantech-p/4709