Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Decomposing complete equipartite multigraphs into cycles of variable
  lengths: the amalgamation-detachment approach   Using the technique of amalgamation-detachment, we show that the complete
equipartite multigraph $\lambda K_{n\times m}$ can be decomposed into cycles of
lengths $c_1m,\dots,c_km$ (plus a 1-factor if the degree is odd) whenever there
exists a decomposition of $\lambda m K_n$ into cycles of lengths $c_1,
\dots,c_k$ (plus a 1-factor if the degree is odd). In addition, we give
sufficient conditions for the existence of some other, related cycle
decompositions of the complete equipartite multigraph $\lambda K_{n\times m}$.

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The categories of this paper are: q-alg
10
The categories of this paper are: q-bio
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The categories of this paper are: bayes-an
5
The categories of this paper are: gr-qc
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The categories of this paper are: nucl-ex
8
The categories of this paper are: hep-ex
9
The categories of this paper are: nlin
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The categories of this paper are: plasm-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: patt-sol
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The categories of this paper are: adap-org
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The categories of this paper are: acc-phys
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The categories of this paper are: funct-an
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The categories of this paper are: solv-int
0
The categories of this paper are: hep-ph
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The categories of this paper are: stat