Characterization of self-complementary graphs with 2-factors

Let G be a self-complementary graph (s.c.) and π its degree sequence. Then G has a 2-factor if and only if π - 2 is graphic. This is achieved by obtaining a structure theorem regarding s.c. graphs without a 2-factor. Another interesting corollary of the structure theorem is that if G is a s.c. graph of order p?8 with minimum degree at least $\text{p}\text{4}$, then G has a 2-factor and the result is the best possible.