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.
The divisibility theorem for isomorphic factorizations of complete graphs
β Scribed by Frank Harary; Robert W. Robinson; Nicholas C. Wormald
- Publisher
- John Wiley and Sons
- Year
- 1977
- Tongue
- English
- Weight
- 91 KB
- Volume
- 1
- Category
- Article
- ISSN
- 0364-9024
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
## Abstract Let __Z__~__p__~ denote the cyclic group of order __p__ where __p__ is a prime number. Let __X__ = __X__(__Z__~__p__~, __H__) denote the Cayley digraph of __Z__~__p__~ with respect to the symbol __H__. We obtain a necessary and sufficient condition on __H__ so that the complete graph on
## Abstract We show how to find a decomposition of the edge set of the complete graph into regular factors where the degree and edgeβconnectivity of each factor is prescribed. Β© 2003 Wiley Periodicals, Inc. J Graph Theory 43: 132β136, 2003
Let Tp be any tree of order p and A ( T p ) stand for the maximum degree of the vertices of Tp. We prove the following theorem. "If A(Tp) 5 pi, where p > 2i, then Tp is i-placeable in Kp" is true if and only if i = 1, 2, and 3. 0 1996 John Wiley & Sons, Inc. Suppose G is a graph and V ( G ) , E ( G
## 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.