On bipartite 2-factorizations of K(n)-I and the Oberwolfach problem

Bryant, Darryn and Danziger, Peter (2011) On bipartite 2-factorizations of K(n)-I and the Oberwolfach problem. Journal of Graph Theory, 68 1: 22-37. doi:10.1002/jgt.20538


Author Bryant, Darryn
Danziger, Peter
Title On bipartite 2-factorizations of K(n)-I and the Oberwolfach problem
Formatted title
On bipartite 2-factorizations of Kn − I and the Oberwolfach problem
Journal name Journal of Graph Theory   Check publisher's open access policy
ISSN 0364-9024
1097-0118
Publication date 2011-09-01
Year available 2010
Sub-type Article (original research)
DOI 10.1002/jgt.20538
Open Access Status Not yet assessed
Volume 68
Issue 1
Start page 22
End page 37
Total pages 16
Place of publication Hoboken, NJ, U.S.A.
Publisher John Wiley & Sons
Language eng
Abstract It is shown that if F-1, F-2, ... , F-t are bipartite 2-regular graphs of order n and alpha(1), alpha(2),..., alpha(t) are positive integers such that alpha(1)+ alpha(2) + ... + alpha(t) = (n-2)/2, alpha(1)>= 3 is odd, and alpha(i) is even for i = 2, 3,..., t, then there exists a 2-factorization of K-n-I in which there are exactly alpha(i) 2-factors isomorphic to F-i for i = 1, 2,..., t. This result completes the solution of the Oberwolfach problem for bipartite 2-factors. (C) 2010 Wiley Periodicals, Inc. J Graph Theory 68: 22-37, 2011
Formatted abstract
It is shown that if F1, F2, …, Ft are bipartite 2-regular graphs of order n and α1, α2, …, αt are positive integers such that α1 + α2 + ⋯ + αt = (n − 2)/2, α1≥3 is odd, and αi is even for i = 2, 3, …, t, then there exists a 2-factorization of KnI in which there are exactly αi 2-factors isomorphic to Fi for i = 1, 2, …, t. This result completes the solution of the Oberwolfach problem for bipartite 2-factors.
Keyword Oberwolfach problem
2-Factorizations
Graph factorizations
Graph decompositions
Hamilton-Waterloo problem
Triangle-factors
Length cycles
Graphs
Decomposition
Q-Index Code C1
Q-Index Status Confirmed Code
Grant ID DP0770400
OGP0170220
Institutional Status UQ
Additional Notes Article first published online: 12 NOV 2010

Document type: Journal Article
Sub-type: Article (original research)
Collections: School of Mathematics and Physics
Official 2012 Collection
 
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