Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Counting perfect matchings and the switch chain   We examine the problem of exactly or approximately counting all perfect
matchings in hereditary classes of nonbipartite graphs. In particular, we
consider the switch Markov chain of Diaconis, Graham and Holmes. We determine
the largest hereditary class for which the chain is ergodic, and define a large
new hereditary class of graphs for which it is rapidly mixing. We go on to show
that the chain has exponential mixing time for a slightly larger class. We also
examine the question of ergodicity of the switch chain in a arbitrary graph.
Finally, we give exact counting algorithms for three classes.

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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: nlin
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The categories of this paper are: nucl-th
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The categories of this paper are: eess
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The categories of this paper are: plasm-ph
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The categories of this paper are: econ
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The categories of this paper are: patt-sol
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The categories of this paper are: bayes-an
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The categories of this paper are: chao-dyn
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The categories of this paper are: cond-mat
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The categories of this paper are: solv-int
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The categories of this paper are: atom-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: ao-sci
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The categories of this paper are: astro-ph