Half-graphs, other non-stable degree sequences, and the switch Markov chain
Abstract
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 -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 -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.
Cite
@article{arxiv.1909.02308,
title = {Half-graphs, other non-stable degree sequences, and the switch Markov chain},
author = {Péter L. Erdős and Ervin Győri and Tamás Róbert Mezei and István Miklós and Dániel Soltész},
journal= {arXiv preprint arXiv:1909.02308},
year = {2021}
}
Comments
Generalized the main theorem, paper extended with a number of corroborating results