Let n ≥ 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 ≡ 2,4 mod 8. We also show that
✦ LIBER ✦
Decomposition of the complete graph plus a 1-factor into cycles of equal length
✍ Scribed by Mateja Šajna
- Publisher
- John Wiley and Sons
- Year
- 2003
- Tongue
- English
- Weight
- 354 KB
- Volume
- 11
- Category
- Article
- ISSN
- 1063-8539
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✦ Synopsis
Abstract
We determine the necessary and sufficient conditions for the existence of a decomposition of the complete graph of even order with a 1‐factor added into cycles of equal length. © 2003 Wiley Periodicals, Inc. J Combin Designs 11: 170–207, 2003; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/jcd.10019
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