Dyer, M orcid.org/0000-0002-2018-0374 and Muller, H orcid.org/0000-0002-1123-1774 (2019) Counting Perfect Matchings and the Switch Chain. SIAM Journal on Discrete Mathematics, 33 (3). pp. 1146-1174. ISSN 0895-4801
Abstract
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 an arbitrary graph. Finally, we give exact counting algorithms for three classes.
Metadata
Item Type: | Article |
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Authors/Creators: | |
Copyright, Publisher and Additional Information: | © 2019, Society for Industrial and Applied Mathematics. This is an author produced version of an article published in SIAM Journal on Discrete Mathematics. Uploaded in accordance with the publisher's self-archiving policy. |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Computing (Leeds) |
Funding Information: | Funder Grant number EPSRC (Engineering and Physical Sciences Research Council) EP/S016562/1 |
Depositing User: | Symplectic Publications |
Date Deposited: | 13 Jun 2019 08:57 |
Last Modified: | 01 Jul 2020 20:28 |
Status: | Published |
Publisher: | Society for Industrial and Applied Mathematics |
Identification Number: | 10.1137/18M1172910 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:137388 |