Packing degenerate graphs
Peter Allen, Julia B\"ottcher, Jan Hladk\'y, Diana Piguet

TL;DR
The paper proves that a large family of sparse, degenerate graphs with bounded degrees can be packed into a complete graph, using a random greedy algorithm, correcting a previous error.
Contribution
It introduces a new packing result for degenerate graphs with bounded degrees, analyzed through a natural random greedy algorithm, improving understanding of graph packing.
Findings
Large families of degenerate graphs can be packed into complete graphs.
The packing is achieved via a natural random greedy algorithm.
A correction to a previously published proof is provided.
Abstract
Given and , whenever is sufficiently small and sufficiently large, if is a family of -degenerate graphs of individual orders at most , maximum degrees at most , and total number of edges at most , then packs into the complete graph . 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].
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