Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Optimal packings of bounded degree trees   We prove that if $T_1,\dots, T_n$ is a sequence of bounded degree trees so
that $T_i$ has $i$ vertices, then $K_n$ has a decomposition into $T_1,\dots,
T_n$. This shows that the tree packing conjecture of Gy\'arf\'as and Lehel from
1976 holds for all bounded degree trees (in fact, we can allow the first $o(n)$
trees to have arbitrary degrees). Similarly, we show that Ringel's conjecture
from 1963 holds for all bounded degree trees. We deduce these results from a
more general theorem, which yields decompositions of dense quasi-random graphs
into suitable families of bounded degree graphs. Our proofs involve
Szemer\'{e}di's regularity lemma, results on Hamilton decompositions of robust
expanders, random walks, iterative absorption as well as a recent blow-up lemma
for approximate decompositions.

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The categories of this paper are: hep-th
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The categories of this paper are: gr-qc
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The categories of this paper are: hep-ex
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The categories of this paper are: dg-ga
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The categories of this paper are: comp-gas
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The categories of this paper are: quant-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: nucl-th
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The categories of this paper are: mtrl-th
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The categories of this paper are: patt-sol
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The categories of this paper are: stat
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The categories of this paper are: supr-con
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The categories of this paper are: cmp-lg
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The categories of this paper are: solv-int
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The categories of this paper are: chao-dyn
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The categories of this paper are: bayes-an