Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Switch-based Markov Chains for Sampling Hamiltonian Cycles in Dense
  Graphs   We consider the irreducibility of switch-based Markov chains for the
approximate uniform sampling of Hamiltonian cycles in a given undirected dense
graph on $n$ vertices. As our main result, we show that every pair of
Hamiltonian cycles in a graph with minimum degree at least $n/2+7$ can be
transformed into each other by switch operations of size at most $10$, implying
that the switch Markov chain using switches of size at most $10$ is
irreducible. As a proof of concept, we also show that this Markov chain is
rapidly mixing on dense monotone graphs.

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The categories of this paper are: funct-an
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The categories of this paper are: q-bio
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The categories of this paper are: patt-sol
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The categories of this paper are: astro-ph
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The categories of this paper are: math-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: hep-th
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The categories of this paper are: nlin
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The categories of this paper are: gr-qc
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The categories of this paper are: stat
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The categories of this paper are: nucl-ex
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The categories of this paper are: bayes-an
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The categories of this paper are: adap-org
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The categories of this paper are: mtrl-th
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The categories of this paper are: q-alg
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The categories of this paper are: solv-int