Work

Generalizations of k-dimensional Weisfeiler–Leman stabilization

Year: 2020

Type: article

Abstract: The family of Weisfeiler-Leman equivalences on graphs is a widely studied approximation of graph isomorphism with many different characterizations. We study these, and other approximations of isomorphism defined in terms of refinement operators and Schurian Polynomial Approximation Schemes (SPAS). The general framework of SPAS allows us to study a number of parameters of the refinement operators based on Weisfeiler-Leman refinement, logic with counting, lifts of Weisfeiler-Leman as defined by Evdokimov and Ponomarenko, and the invertible map test introduced by Dawar and Holm, and variations of these, and establish relationships between them.

Source: Moscow Journal of Combinatorics and Number Theory

DOI: 10.2140/moscow.2020.9.229

Authors: Anuj Dawar, Danny Vagnozzi

Institution: University of Cambridge

Language: English

Topic: Advanced Graph Theory Research

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

Funder: Engineering and Physical Sciences Research Council

Awards: Resources and co-resources: a junction between semantics and descriptive complexity, Circuits, Logic and Symmetry, Algebraic Methods in the Study of Graph Isomorphism