Work

The ineffectiveness of the regularity lemma for bounded degree graphs

Year: 2025

Type: article

Abstract: We show that for any , there is no bound computable from on the size of a graph required to approximate a graph of maximum degree at most up to error in ‐neighborhood statistics. This provides a negative answer to a question posed by Lovász. Our result is a direct consequence of the recent celebrated work of Bowen, Chapman, Lubotzky, and Vidick, which refutes the Aldous–Lyons conjecture.

Source: Bulletin of the London Mathematical Society

DOI: 10.1112/blms.70176

Authors: Clark Lyons, Grigory Terlov, Zoltán Vidnyánszky

Institutions: HUN-REN Alfréd Rényi Institute of Mathematics, Hungarian Research Network, University of North Carolina at Chapel Hill, Eötvös Loránd University

Language: English

Topic: Limits and Structures in Graph Theory

Subfield: Discrete Mathematics and Combinatorics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Hawaii Academy of Science, European Research Council, National Research, Development and Innovation Office

Awards: G350592136, G5435431566, G7193725192