Half-Graphs, Other Non-stable Degree Sequences, and the Switch Markov Chain

Half-Graphs, Other Non-stable Degree Sequences, and the Switch Markov Chain

One of the simplest methods of generating a random graph with a given degree sequence is provided by the Monte Carlo Markov Chain method using switches. The switch Markov chain converges to the uniform distribution, but generally the rate of convergence is not known. After a number of results concer...

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Veröffentlicht in:The Electronic journal of combinatorics 2021-07, Vol.28 (3)
Hauptverfasser: Erdős, Péter L., Győri, Ervin, Mezei, Tamás Róbert, Miklós, István, Soltész, Dániel
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container_title The Electronic journal of combinatorics
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creator Erdős, Péter L.
Győri, Ervin
Mezei, Tamás Róbert
Miklós, István
Soltész, Dániel
description One of the simplest methods of generating a random graph with a given degree sequence is provided by the Monte Carlo Markov Chain method using switches. The switch Markov chain converges to the uniform distribution, but generally the rate of convergence is not known. After a number of results concerning various degree sequences, rapid mixing was established for so-called P-stable degree sequences (including that of directed graphs), which covers every previously known rapidly mixing region of degree sequences. In this paper we give a non-trivial family of degree sequences that are not P-stable and the switch Markov chain is still rapidly mixing on them. This family has an intimate connection to Tyshkevich-decompositions and strong stability as well.
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title Half-Graphs, Other Non-stable Degree Sequences, and the Switch Markov Chain
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