Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Hamilton decompositions of line graphs   It is proved that if a graph is regular of even degree and contains a
Hamilton cycle, or regular of odd degree and contains a Hamiltonian $3$-factor,
then its line graph is Hamilton decomposable. This result partially extends
Kotzig's result that a $3$-regular graph is Hamiltonian if and only if its line
graph is Hamilton decomposable, and proves the conjecture of Bermond that the
line graph of a Hamilton decomposable graph is Hamilton decomposable.

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The categories of this paper are: q-alg
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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: acc-phys
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The categories of this paper are: supr-con
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The categories of this paper are: alg-geom
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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: solv-int
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The categories of this paper are: q-fin
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The categories of this paper are: ao-sci
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The categories of this paper are: adap-org
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The categories of this paper are: cond-mat
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The categories of this paper are: eess
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The categories of this paper are: math-ph
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The categories of this paper are: cs