Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Making multigraphs simple by a sequence of double edge swaps   We show that any loopy multigraph with a graphical degree sequence can be
transformed into a simple graph by a finite sequence of double edge swaps with
each swap involving at least one loop or multiple edge. Our result answers a
question of Janson motivated by random graph theory, and it adds to the rich
literature on reachability of double edge swaps with applications in Markov
chain Monte Carlo sampling from the uniform distribution of graphs with
prescribed degrees.

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The categories of this paper are: quant-ph
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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: atom-ph
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The categories of this paper are: eess
0
The categories of this paper are: hep-ph
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The categories of this paper are: econ
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The categories of this paper are: nlin
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The categories of this paper are: q-alg
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The categories of this paper are: comp-gas
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The categories of this paper are: plasm-ph
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The categories of this paper are: hep-th
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The categories of this paper are: chao-dyn
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The categories of this paper are: dg-ga
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The categories of this paper are: alg-geom