On bipartite 2-factorizations of kn − I and the Oberwolfach problem

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 Kn − I in which there are exactly αi 2‐factors isomorphic...

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Bibliographic Details
Published in:Journal of graph theory 2011-09, Vol.68 (1), p.22-37
Main Authors: Bryant, Darryn, Danziger, Peter
Format: Article
Language:English
Subjects:
2-factorizations
graph decompositions
graph factorizations
Oberwolfach problem
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Summary: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 Kn − I 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. © 2010 Wiley Periodicals, Inc. J Graph Theory 68:22‐37, 2011
ISSN:0364-9024
1097-0118
DOI:10.1002/jgt.20538