Some sufficient conditions are proven for the complete graph of even order with a 1-factor removed to be decomposable into even length cycles. 0 1994 John Wiley & Sons, Inc. ## 1. Introduction It is natural to ask when a complete graph admits a decomposition into cycles of some fixed length. Since
Cycle decompositions of complete graphs
β Scribed by E.J. Farrell
- Publisher
- Elsevier Science
- Year
- 1982
- Tongue
- English
- Weight
- 447 KB
- Volume
- 38
- Category
- Article
- ISSN
- 0012-365X
No coin nor oath required. For personal study only.
β¦ Synopsis
The circuit polynomial c%f the complete graph K, is used to deduce results about nodedisjoint -vcle decompositiorls of K,, satisfying variow restrictions.
π SIMILAR VOLUMES
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
## Abstract We construct a new symmetric Hamilton cycle decomposition of the complete graph __K~n~__ for odd __n__β>β7. Β© 2003 Wiley Periodicals, Inc.
## Abstract For all odd integers __n__ββ₯β1, let __G~n~__ denote the complete graph of order __n__, and for all even integers __n__ββ₯β2 let __G~n~__ denote the complete graph of order __n__ with the edges of a 1βfactor removed. It is shown that for all nonβnegative integers __h__ and __t__ and all p
## Abstract We determine the necessary and sufficient conditions for the existence of a decomposition of the complete graph of even order with a 1βfactor added into cycles of equal length. Β© 2003 Wiley Periodicals, Inc. J Combin Designs 11: 170β207, 2003; Published online in Wiley InterScience (www
## Abstract We show that the necessary conditions for the decomposition of the complete graph of odd order into cycles of a fixed even length and for the decomposition of the complete graph of even order minus a 1βfactor into cycles of a fixed odd length are also sufficient. Β© 2002 John Wiley & Son