Abstract:We prove that there is $c>0$ such that for all sufficiently large $n$, if $T_1,\dots,T_n$ are any trees such that $T_i$ has $i$ vertices and maximum degree at most $cn/\log n$, then $\{T_1,\dots,T_n\}$ packs into $K_n$. Our main result actually allows to replace the host graph $K_n$ by an arbitrary quasirandom graph, and to generalize from trees to graphs of bounded degeneracy that are rich in bare paths, contain some odd degree vertices, and only satisfy much less stringent restrictions on their number of vertices.
From: Jan Hladky [view email]
[v1]
Tue, 22 Jun 2021 12:39:46 UTC (253 KB)
[v2]
Mon, 20 Jun 2022 12:27:14 UTC (247 KB)
[v3]
Tue, 8 Sep 2026 20:00:49 UTC (309 KB)
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