Dvorak-Dell-Grohe-Rattan theorem via an asymptotic argument
Combinatorics
2025-07-22 v1 Discrete Mathematics
Data Structures and Algorithms
Abstract
Two graphs are distinguished by the Weisfeiler--Leman isomorphism test if and only if there is a tree that has a different number of homomorphisms to and to . There are two known proofs of this fact -- a logical proof by Dvorak and a linear-algebraic proof by Dell, Grohe, and Rattan. We give another simple proof, based on ordering WL-labels and asymptotic arguments.
Cite
@article{arxiv.2507.14669,
title = {Dvorak-Dell-Grohe-Rattan theorem via an asymptotic argument},
author = {Alexander Kozachinskiy},
journal= {arXiv preprint arXiv:2507.14669},
year = {2025}
}