Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Decompositions of highly connected graphs into paths of length five   We study the Decomposition Conjecture posed by Bar\'at and Thomassen (2006),
which states that for every tree $T$ there exists a natural number $k_T$ such
that, if $G$ is a $k_T$-edge-connected graph and $|E(T)|$ divides $|E(G)|$,
then $G$ admits a decomposition into copies of $T$. In a series of papers,
Thomassen verified this conjecture for stars, some bistars, paths of length
$3$, and paths whose length is a power of $2$. We verify the Decomposition
Conjecture for paths of length $5$.

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The categories of this paper are: nlin
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The categories of this paper are: hep-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: cond-mat
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The categories of this paper are: dg-ga
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The categories of this paper are: quant-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: nucl-th
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The categories of this paper are: q-bio
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The categories of this paper are: bayes-an
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The categories of this paper are: hep-th
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The categories of this paper are: adap-org
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The categories of this paper are: mtrl-th
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The categories of this paper are: cs
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The categories of this paper are: hep-lat
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The categories of this paper are: solv-int