# Wilson's Theorem

### From G-designs

# Wilson's Theorem

**Theorem**
_{[1]}

*For any given graph , there exists an integer ( is exponentially large) such that if*

*;**; and**where is the greatest common divisor of the degrees of the vertices in ,*

then there exists a -design of order .

- ↑ Wilson, R. M.
*Decompositions of complete graphs into subgraphs isomorphic to a given graph*, Proceedings of the Fifth British Combinatorial Conference (Univ. Aberdeen, Aberdeen, 1975), Congressus Numerantium, No. XV, Utilitas Math., Winnipeg, Man. 647–659 (1976).