EMBEDDING ARBITRARY GRAPHS OF MAXIMUM DEGREE 2

Let delta(H) be the minimum degree of the graph H. We prove that a gra ph H of order n with delta(H) greater-than-or-equal-to (2n-1)/3 contai ns any graph G of order at most n and maximum degree DELTA(G) less-tha n-or-equal-to 2 as a subgraph, and this bound is best possible. Furthe rmore, this result settles the case DELTA(G) = 2 of the well-known con jecture of Bollobas, Catlin and Eldridge on packing two graphs with gi ven maximum degree.