Work

Randomly Twisted Hypercubes: Between Structure and Randomness

Year: 2024

Type: article

Abstract: 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.

Source: Random Structures and Algorithms

DOI: 10.1002/rsa.21267

Authors: Itai Benjamini, Yotam Dikstein, Renan Gross, Maksim Zhukovskii

Institutions: Weizmann Institute of Science, Tel Aviv University

Language: English

Topic: Limits and Structures in Graph Theory

Subfield: Discrete Mathematics and Combinatorics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $4,330

Funders: Israel Academy of Sciences and Humanities, Israel Science Foundation, H2020 European Research Council