Benjamini, I., Dikstein, Y., Gross, R. orcid.org/0009-0007-5880-7033 et al. (1 more author) (2025) Randomly twisted hypercubes: between structure and randomness. Random Structures & Algorithms, 66 (1). e21267. ISSN 1042-9832
Abstract
Twisted hypercubes are generalizations of the Boolean hypercube, obtained by iteratively connecting two instances of a graph by a uniformly random perfect matching. Dudek et al. showed that when the two instances are independent, these graphs have optimal diameter. We study twisted hypercubes in the setting where the instances can have general dependence, and also in the particular case where they are identical. We show that the resultant graph shares properties with random regular graphs, including small diameter, large vertex expansion, a semicircle law for its eigenvalues and no non-trivial automorphisms. However, in contrast to random regular graphs, twisted hypercubes allow for short routing schemes.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2024 The Author(s). Random Structures & Algorithms published by Wiley Periodicals LLC. This is an open access article under the terms of the Creative Commons Attribution License, (http://creativecommons.org/licenses/by/4.0/) which permits use, distribution and reproduction in any medium, provided the original work is properly cited. |
Keywords: | random graphs; semicircle law; shortest path; vertex expansion |
Dates: |
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Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Faculty of Engineering (Sheffield) > Department of Computer Science (Sheffield) |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 13 Dec 2024 14:22 |
Last Modified: | 13 Dec 2024 14:22 |
Status: | Published |
Publisher: | Wiley |
Refereed: | Yes |
Identification Number: | 10.1002/rsa.21267 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:220363 |