Hamilton cycle rich two-factorizations of complete graphs

Bryant, D (2004) Hamilton cycle rich two-factorizations of complete graphs. Journal of Combinatorial Designs, 12 2: 147-155. doi:10.1002/jcd.20005

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Author Bryant, D
Title Hamilton cycle rich two-factorizations of complete graphs
Journal name Journal of Combinatorial Designs   Check publisher's open access policy
ISSN 1063-8539
Publication date 2004-01-01
Sub-type Article (original research)
DOI 10.1002/jcd.20005
Volume 12
Issue 2
Start page 147
End page 155
Total pages 9
Editor C. Colbourn
Place of publication United States of America
Publisher John Wiley & Sons, Inc
Language eng
Subject C1
230101 Mathematical Logic, Set Theory, Lattices And Combinatorics
780101 Mathematical sciences
Formatted abstract
For all integers n ≥ 5, it is shown that the graph obtained from the n-cycle by joining vertices at distance 2 has a 2-factorization is which one 2-factor is a Hamilton cycle, and the other is isomorphic to any given 2-regular graph of order n. This result is used to prove several results on 2-factorizations of the complete graph Kn of order n. For example, it is shown that for all odd n ≥ 11, Kn has a 2-factorization in which three of the 2-factors are isomorphic to any three given 2-regular graphs of order n, and the remaining 2-factors are Hamilton cycles. For any two given 2-regular graphs of even order n, the corresponding result is proved for the graph Kn - I obtained from the complete graph by removing the edges of a 1-factor.
© 2004 Wiley Periodicals, Inc.
Keyword 2-Factorization
Hamilton cycle decomposition
Graph decomposition
Graph factorization
Oberwolfach problem
Cayley graphs
Q-Index Code C1

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Created: Wed, 15 Aug 2007, 12:59:20 EST