Embedding (p,p−1) graphs in their complements

AbstractA graphG is embeddable in its complement $$\bar G$$ ifG is isomorphic with a subgraph of $$\bar G$$ . A complete characterization is given of those (p,p−1) graphs which are embeddable in their complements. In particular, letG be a (p,p−1) graph wherep≧6 ifp is even andp≧9 ifp is odd; thenG is embeddable in $$\bar G$$ if and only ifG is neither the starK1,p−1 norK1,n∪C3 withn≧4.