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.