There is some hint that 2 may be special with respect to the partition
result proved above. Namely, if 2 divides the number of edges of *K*_{n}and the valence is even, that is,
,
there is
a partition of the edge set of *K*_{n} into two isomorphic circulants
if and only if all primes dividing n are congruent to 1 modulo 4.

Is there some extension of the result to other *k*>2. If *k*>2, it
is easy to construct partitions of the edge set of *K*_{n} into *k*isomorphic circulant graphs if every prime dividing *n* is congruent
to 1 modulo 2*k*. However, this condition is no longer necessary.
For example, the edges of *K*_{15} can be partitioned into seven
Hamilton cycles. They are certainly circulant graphs, but 15 is
not a product of primes congruent to 1 modulo 14.

This suggests an obvious question. One also may want to require that
the circulant subgraphs span *K*_{n}.