Dvorak-Dell-Grohe-Rattan theorem via an asymptotic argument
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866909696654311424 |
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| author | Kozachinskiy, Alexander |
| author_facet | Kozachinskiy, Alexander |
| contents | Two graphs $G_1,G_2$ are distinguished by the Weisfeiler--Leman isomorphism test if and only if there is a tree $T$ that has a different number of homomorphisms to $G_1$ and to $G_2$. 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_14669 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Dvorak-Dell-Grohe-Rattan theorem via an asymptotic argument Kozachinskiy, Alexander Combinatorics Discrete Mathematics Data Structures and Algorithms Two graphs $G_1,G_2$ are distinguished by the Weisfeiler--Leman isomorphism test if and only if there is a tree $T$ that has a different number of homomorphisms to $G_1$ and to $G_2$. 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. |
| title | Dvorak-Dell-Grohe-Rattan theorem via an asymptotic argument |
| topic | Combinatorics Discrete Mathematics Data Structures and Algorithms |
| url | https://arxiv.org/abs/2507.14669 |