A note on the colour class of a self-complementary graph Original Research Article

We prove that any self-complementary graph G contains no proper overfull subgraph H such that Δ(H)=Δ(G) and |V(H)|<|V(G)|. Moreover, a self-complementary graph G is overfull if, and only if, it is regular. This is a support for the following conjecture: a self-complementary graph G is Class 2 if, and only if, G is regular.