Packing d-degenerate graphs

We study packings of graphs with given maximal degree. We shall prove that the (hitherto unproved) Bollobas-Eldridge-Catlin Conjecture holds in a considerably stronger form if one of the graphs is d-degenerate for d not too large: if d, Delta(1), Delta(2) >= 1 and n > max(40 Delta(1) 1n Delta(2), 40d Delta(2)) then a d-degenerate graph of maximal degree Delta(1) and a graph of order n and maximal degree Delta(2) pack. We use this result to show that, for d fixed and n large enough, one can pack n/1500d(2) arbitrary d-degenerate n-vertex graphs of maximal degree at most n/1000d 1n n. (c) 2007 Elsevier Inc. All rights reserved.