On the number of 1-factorizations of the complete graph
β Scribed by Charles C Lindner; Eric Mendelsohn; Alexander Rosa
- Publisher
- Elsevier Science
- Year
- 1976
- Tongue
- English
- Weight
- 929 KB
- Volume
- 20
- Category
- Article
- ISSN
- 0095-8956
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
Extending a result by Hartman and Rosa (1985, Europ. J. Combinatorics 6, 45-48), we prove that for any Abelian group G of even order, except for G Z 2 n with n > 2, there exists a onefactorization of the complete graph admitting G as a sharply-vertex-transitive automorphism group.
## Abstract It is known that a necessary condition for the existence of a 1βrotational 2βfactorization of the complete graph __K__~2__n__+1~ under the action of a group __G__ of order 2__n__ is that the involutions of __G__ are pairwise conjugate. Is this condition also sufficient? The complete ans
We present a necessary condition for a complete bipartite graph K,., to be K,.,-factorizable and a sufficient condition for K,,, to have a K,,,-factorization whenever k is a prime number. These two conditions provide Ushio's necessary and sufficient condition for K,,, to have a K,,,-factorization.
## Abstract We give some simple characterizations of those __n__ for which __K~n~__ has a sharply transitive 1βfactorization with an assigned automorphism group that acts sharply transitively on the vertex set and also fixes a 1βfactor. Β© 1994 John Wiley & Sons, Inc.