Let n β₯ 2 be an integer. The complete graph K n with a 1-factor F removed has a decomposition into Hamilton cycles if and only if n is even. We show that K n -F has a decomposition into Hamilton cycles which are symmetric with respect to the 1-factor F if and only if n β‘ 2,4 mod 8. We also show that
Symmetric Hamilton cycle decompositions of the complete graph
β Scribed by Jin Akiyama; Midori Kobayashi; Gisaku Nakamura
- Publisher
- John Wiley and Sons
- Year
- 2003
- Tongue
- English
- Weight
- 95 KB
- Volume
- 12
- Category
- Article
- ISSN
- 1063-8539
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β¦ Synopsis
Abstract
We construct a new symmetric Hamilton cycle decomposition of the complete graph K~n~ for odd nβ>β7. Β© 2003 Wiley Periodicals, Inc.
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