A 1-factorization of the line graphs of complete graphs
β Scribed by Brian Alspach
- Publisher
- John Wiley and Sons
- Year
- 1982
- Tongue
- English
- Weight
- 254 KB
- Volume
- 6
- Category
- Article
- ISSN
- 0364-9024
No coin nor oath required. For personal study only.
β¦ Synopsis
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.
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 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
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.
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