Proof of the Bollobas-Catlin-Eldridge conjecture We say that two graphs G and H pack if G and H can be embedded into the same vertex set such that the images of the edge sets do not overlap. Bollobas and Eldridge, and independently Catlin conjectured that if the graphs G and H on n vertices with maximum degree M(G) and M(H), respectively, satisfy (M(G) + 1)(M(H) + 1) d n + 1 then G and H pack. Aigner and Brandt and, independently, Alon and Fischer proved this in the case M(G),M(H) < 3, Csaba, Shokoufandeh and Szemeredi proved the conjecture if M(G),M(H) < 4. Bollobas, Kostochka and Nakprasit settled the case when one of the graphs is degenerate. Kaul, Kostochka and Yu showed that if M(G)M(H) < 3/5n and the maximal degrees are large enough then G and H pack. We prove the conjecture for graphs with at least 10^8 vertices.