Given $D$ and $\gamma>0$, whenever $c>0$ is sufficiently small and $n$ sufficiently large, if $\mathcal{ G}$ is a family of $D$-degenerate graphs of individual orders at most $n$, maximum degrees at most $\tfrac{ cn}{ \log n}$, and total number of edges at most $(1-\gamma)\binom{ n}{ 2}$, then $\mathcal{ G}$ packs into the complete graph $K_{ n}$. Our proof proceeds by analysing a natural random greedy packing algorithm. This version of the manuscript corrects a small error that appeared in the published version [Adv Math, 354 (2019), 106739].
Categories: math.CO