Cooper, C, Dyer, M orcid.org/0000-0002-2018-0374 and Greenhill, C (2021) A Triangle Process on Regular Graphs. In: Combinatorial Algorithms. 32nd International Workshop, IWOCA 2021, 05-07 Jul 2021, Ottawa, ON, Canada. , pp. 310-323. ISBN 978-3-030-79986-1
Abstract
Switches are operations which make local changes to the edges of a graph, usually with the aim of preserving the vertex degrees. We study a restricted set of switches, called triangle switches. Each triangle switch creates or deletes at least one triangle. Triangle switches can be used to define Markov chains which generate graphs with a given degree sequence and with many more triangles (3-cycles) than is typical in a uniformly random graph with the same degrees. We show that the set of triangle switches connects the set of all d-regular graphs on n vertices, for all d≥3 . Hence, any Markov chain which assigns positive probability to all triangle switches is irreducible on these graphs. We also investigate this question for 2-regular graphs.
Metadata
Item Type: | Proceedings Paper |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © Springer Nature Switzerland AG 2021. This is an author produced version of an article, published in Combinatorial Algorithms. IWOCA 2021. Lecture Notes in Computer Science. Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | Regular graphs; Triangles; Markov chains; Irreducibility |
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: | 29 Sep 2021 13:03 |
Last Modified: | 30 Jun 2022 00:13 |
Status: | Published |
Identification Number: | 10.1007/978-3-030-79987-8_22 |
Related URLs: | |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:178589 |