Isomorphic factorization colors the edges a given graph 
with 
colors so that the colored subgraphs are isomorphic.
The graph 
is then 
-splittable,
with 
as the divisor, and the subgraph as the factor.
When a complete graph is 2-split, a self-complementary graph results. Similarly, an 
-regular class
1 graph can be 
-split into graphs consisting of disconnected edges, making
the edge chromatic number.
The complete graph 
can be 3-split into identical planar
graphs.
Some Ramsey numbers have been bounded via isomorphic factorizations. For instance, the complete graph 
has the Clebsch graph as a factor, proving 
(Gardner 1989). That is, the complete graph on 16 points can be three-colored so
that no triangle of a single color appears. (In 1955, 
was proven.)
In addition, 
can be 8-split with the Petersen graph as a factor,
or 5-split with a doubled cubical graph as a factor
(shown by Exoo in 2005).
The Hoffman-Singleton graph is 7-splittable into edges (shown by Royle in 2004). Whether the Hoffman-Singleton
graph is a factor of 
via another 7-split is an unsolved
problem.
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