## Abstract We consider oneβfactorizations of __K__~2__n__~ possessing an automorphism group acting regularly (sharply transitively) on vertices. We present some upper bounds on the number of oneβfactors which are fixed by the group; further information is obtained when equality holds in these boun
On the size of graphs with complete-factors
β Scribed by Jin Akiyama; Peter Frankl
- Publisher
- John Wiley and Sons
- Year
- 1985
- Tongue
- English
- Weight
- 188 KB
- Volume
- 9
- Category
- Article
- ISSN
- 0364-9024
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
## Abstract A cube factorization of the complete graph on __n__ vertices, __K~n~__, is a 3βfactorization of __K~n~__ in which the components of each factor are cubes. We show that there exists a cube factorization of __K~n~__ if and only if __n__ β‘ 16 (mod 24), thus providing a new family of unifor
## Abstract A 1βfactorization is constructed for the line graph of the complete graph __K~n~__ when __n__ is congruent to 0 or 1 modulo 4.
We give necessary and sufficient conditions that the complete graph K, has an isomorphic factorization into Kr X K,. We show that this factorization has an application to clone library screening.
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.