On one-factorizations of the complete graph
β Scribed by L Pyber
- Publisher
- Elsevier Science
- Year
- 1987
- Tongue
- English
- Weight
- 66 KB
- Volume
- 67
- Category
- Article
- ISSN
- 0012-365X
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π SIMILAR VOLUMES
## 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
In this paper we use Tutte's f-factor theorem and the method of amalgamations to find necessary and sufficient conditions for the existence of a k-factor in the complete multipartite graph K(p(1 ) ..... p(n)), conditions that are reminiscent of the Erd6s-Gallai conditions for the existence of simple
## Abstract We consider 2βfactorizations of complete graphs that possess an automorphism group fixing __k__β©Ύ0 vertices and acting sharply transitively on the others. We study the structures of such factorizations and consider the cases in which the group is either abelian or dihedral in some more d
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.