Work

The diameter of random Schreier graphs

Year: 2025

Type: article

Abstract: We give a combinatorial proof of the following theorem. Let G be any finite group acting transitively on a set of cardinality n . If S ⊆ G is a random set of size k , with k ≥ ( log n ) 1 + ɛ for some ɛ > 0 , then the diameter of the corresponding Schreier graph is O ( log k n ) with high probability. Except for the implicit constant, this result is the best possible.

Source: European Journal of Combinatorics

DOI: 10.1016/j.ejc.2025.104164

Authors: Daniele Dona, Luca Sabatini

Institutions: HUN-REN Alfréd Rényi Institute of Mathematics, University of Warwick

Language: English

Topic: Finite Group Theory Research

Subfield: Discrete Mathematics and Combinatorics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,560

Funders: Royal Society, Mathematisches Forschungsinstitut Oberwolfach, Leibniz-Gemeinschaft