# 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, DarrynDanziger, Peter On bipartite 2-factorizations of K(n)-I and the Oberwolfach problem On bipartite 2-factorizations of Kn − I and the Oberwolfach problem Journal of Graph Theory   Check publisher's open access policy 0364-90241097-0118 2011-09-01 2010 Article (original research) 10.1002/jgt.20538 Not yet assessed 68 1 22 37 16 Hoboken, NJ, U.S.A. John Wiley & Sons eng 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 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. Oberwolfach problem2-FactorizationsGraph factorizationsGraph decompositionsHamilton-Waterloo problemTriangle-factorsLength cyclesGraphsDecomposition C1 Confirmed Code DP0770400OGP0170220 UQ Article first published online: 12 NOV 2010

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

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