Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Resolvable Cycle Decompositions of Complete Multigraphs and Complete
  Equipartite Multigraphs via Layering and Detachment   We construct new resolvable decompositions of complete multigraphs and
complete equipartite multigraphs into cycles of variable lengths (and a perfect
matching if the vertex degrees are odd). We develop two techniques: {\em
layering}, which allows us to obtain 2-factorizations of complete multigraphs
from existing 2-factorizations of complete graphs, and {\em detachment}, which
allows us to construct resolvable cycle decompositions of complete equipartite
multigraphs from existing resolvable cycle decompositions of complete
multigraphs. These techniques are applied to obtain new 2-factorizations of a
specified type for both complete multigraphs and complete equipartite
multigraphs, with the emphasis on new solutions to the Oberwolfach Problem and
the Hamilton-Waterloo Problem. In addition, we show existence of some
$\alpha$-resolvable cycle decompositions.

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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-ph
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The categories of this paper are: dg-ga
3
The categories of this paper are: physics
13
The categories of this paper are: quant-ph
36
The categories of this paper are: cmp-lg
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The categories of this paper are: q-alg
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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: stat
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The categories of this paper are: mtrl-th
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The categories of this paper are: atom-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: nucl-th
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The categories of this paper are: nucl-ex
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The categories of this paper are: patt-sol