Switch-based Markov chains for sampling hamiltonian cycles in dense graphs

Pieter Kleer, V. Patel, Fabian Stroh

Research output: Contribution to journalArticleScientificpeer-review

Abstract

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.
Original languageEnglish
Article numberP4.29
JournalElectronic Journal of Combinatorics
Volume27
Issue number4
DOIs
Publication statusPublished - Nov 2020
Externally publishedYes

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