Abstract
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 H ¯ 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.
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