A simple, undirected, loopless graph G of order p and size q is called a (p, q) graph. Two graphs G and H of the same order are packable if G can be embedded in the complement of H. Two theorems are proved in this paper. Theorem 1 gives a complete characterization of two (p, p − 1) graphs which are packable. Theorem 2 gives a complete characterization of the pairs {T, G}, where T is a tree of order p and G is a (p, p) graph, that can be packed. Theorem 1 generalizes some earlier results of N. Sauer and J. Spencer, D. Burns and S. Schuster, and P. J. Slater, S. K. Teo and H. P. Yap. Theorem 2 extends an earlier result of P. J. Slater, S. K. Teo and H. P. Yap.
