Packing d-degenerate graphs


We study packings of graphs with given maximal degree. We shall prove that the (hitherto unproved) Bollobás-Eldridge-Catlin Conjecture holds in a considerably stronger form if one of the graphs is d-degenerate for d not too large: if d, Δ1, Δ2 ≥ 1 and n > max {40 Δ1 ln Δ2, 40 d Δ2} then a d-degenerate graph of maximal degree Δ1 and a graph of order n and maximal degree Δ2 pack. We use this result to show that, for d fixed and n large enough, one can pack frac(n, 1500 d2) arbitrary d-degenerate n-vertex graphs of maximal degree at most frac(n, 1000 d ln n). © 2007 Elsevier Inc. All rights reserved.

Publication Title

Journal of Combinatorial Theory. Series B