Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Asymptotically optimal $K_k$-packings of dense graphs via fractional
  $K_k$-decompositions   Let $H$ be a fixed graph. A {\em fractional $H$-decomposition} of a graph $G$
is an assignment of nonnegative real weights to the copies of $H$ in $G$ such
that for each $e \in E(G)$, the sum of the weights of copies of $H$ containing
$e$ in precisely one. An {\em $H$-packing} of a graph $G$ is a set of edge
disjoint copies of $H$ in $G$. The following results are proved. For every
fixed $k > 2$, every graph with $n$ vertices and minimum degree at least
$n(1-1/9k^{10})+o(n)$ has a fractional $K_k$-decomposition and has a
$K_k$-packing which covers all but $o(n^2)$ edges.

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The categories of this paper are: nucl-th
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The categories of this paper are: hep-th
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The categories of this paper are: alg-geom
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The categories of this paper are: nucl-ex
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The categories of this paper are: eess
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The categories of this paper are: cond-mat
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The categories of this paper are: hep-lat
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The categories of this paper are: gr-qc
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The categories of this paper are: quant-ph
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The categories of this paper are: nlin
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The categories of this paper are: q-bio
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The categories of this paper are: solv-int
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The categories of this paper are: adap-org
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The categories of this paper are: astro-ph
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The categories of this paper are: q-fin
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The categories of this paper are: bayes-an