Given D and γ>0, whenever c>0 is sufficiently small and n sufficiently large, if G is a family of D-degenerate graphs of individual orders at most n, maximum degrees at most cnlogn, and total number of edges at most (1−γ)(n2), then G packs into the complete graph Kn. Our proof proceeds by analysing a natural random greedy packing algorithm.
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Allen et al. (2019) studied this question.
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