Work

The diameter of randomly twisted hypercubes

Year: 2024

Type: article

Abstract: The n -dimensional random twisted hypercube G n is constructed recursively by taking two instances of G n − 1 , with any joint distribution, and adding a random perfect matching between their vertex sets. Benjamini, Dikstein, Gross, and Zhukovskii showed that its diameter is O ( n log log log n / log log n ) with high probability and at least ( n − 1 ) / log 2 n . We improve their upper bound by showing that diam ( G n ) = ( 1 + o ( 1 ) ) n log 2 n with high probability.

Source: European Journal of Combinatorics

DOI: 10.1016/j.ejc.2024.104078

Authors: Lucas Aragão, Maurício Collares, Gabriel Dahia, João Pedro Marciano

Institutions: Universidade do Estado do Rio de Janeiro, Instituto Politécnico do Rio de Janeiro, Graz University of Technology, Instituto Nacional de Matemática Pura e Aplicada

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: $3,000

Funders: Coordenação de Aperfeiçoamento de Pessoal de Nível Superior, Austrian Science Fund, Conselho Nacional de Desenvolvimento Científico e Tecnológico