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.

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).