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On bipartite 2‐factorizations of k n − I and the Oberwolfach problem
Author(s) -
Bryant Darryn,
Danziger Peter
Publication year - 2011
Publication title -
journal of graph theory
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 54
eISSN - 1097-0118
pISSN - 0364-9024
DOI - 10.1002/jgt.20538
Subject(s) - bipartite graph , mathematics , combinatorics , complete bipartite graph , factorization , order (exchange) , graph , discrete mathematics , algorithm , finance , economics
It is shown that if F 1 , F 2 , …, F t are bipartite 2‐regular graphs of order n and α 1 , α 2 , …, α t are positive integers such that α 1 + α 2 + ⋅ + α t = ( n − 2)/2, α 1 ≥3 is odd, and α i is even for i = 2, 3, …, t , then there exists a 2‐factorization of K n − I in which there are exactly α 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. © 2010 Wiley Periodicals, Inc. J Graph Theory 68:22‐37, 2011