# The Weisfeiler-Leman Algorithm: An Exploration of its Power

@inproceedings{Kiefer2021TheWA, title={The Weisfeiler-Leman Algorithm: An Exploration of its Power}, author={Sandra Kiefer}, year={2021} }

Some of my favorite open problems concern fixed-point logic with counting, FPC. It is known that counting logic with k + 1 variables, Ck+1, has exactly the same expressive power as the classic k-dimensional Weisfeiler-Leman Algorithm, k-WL. Furthermore, the quantifier-depth of a Ck+1 formula needed to express the color of a k-tuple of vertices is equal to the number of iterations of k-WL needed to derive that color. Much has been learned about FPC and the power of k-WL in the last forty years… Expand

#### 7 Citations

Logarithmic Weisfeiler-Leman Identifies All Planar Graphs

- Computer Science, Mathematics
- ICALP
- 2021

It is shown that there is a constant k such that every planar graph can be identified by the k-dimensional WL algorithm within a logarithmic number of iterations, which implies that everyPlanar graph is definable with a Ck+1-sentence of logarithsmic quantifier depth. Expand

The Power of the Weisfeiler-Leman Algorithm to Decompose Graphs

- Computer Science, Mathematics
- MFCS
- 2019

It is proved that the 2-dimensional Weisfeiler-Leman algorithm implicitly computes the decomposition of a graph into its 3-connected components and insights are obtained about the connectivity of constituent graphs of association schemes. Expand

Lovász-Type Theorems and Game Comonads

- Computer Science, Mathematics
- 2021 36th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)
- 2021

This work proposes a new categorical formulation, which applies to any locally finite category with pushouts and a proper factorisation system, and presents a novel application to homomorphism counts in modal logic. Expand

The Logic of Graph Neural Networks

- Computer Science
- 2021 36th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)
- 2021

This paper explains how the expressiveness of GNNs can be characterised precisely by the combinatorial Weisfeiler-Leman algorithms and by finite variable counting logics. Expand

Graph Learning with 1D Convolutions on Random Walks

- Computer Science
- ArXiv
- 2021

It is demonstrated empirically that CRAWL matches or outperforms state-of-the-art GNN architectures across a multitude of benchmark datasets for classification and regression on graphs. Expand

Recent Advances on the Graph Isomorphism Problem

- Computer Science, Mathematics
- ArXiv
- 2020

The main focus will be on Babai's quasi-polynomial time isomorphism test and subsequent developments that led to the design of isomorphicism algorithms with a quasi- polynomial parameterized running time of the from $n^{\polylog k}$, where $k$ is a graph parameter such as the maximum degree. Expand

Seurat games on Stockmeyer graphs

- Mathematics
- 2020

We define a family of vertex colouring games played over a pair of graphs or digraphs $(G,H)$ by players $\forall$ and $\exists$. These games arise from work on a longstanding open problem in… Expand

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The Power of the Weisfeiler-Leman Algorithm to Decompose Graphs

- Computer Science, Mathematics
- MFCS
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It is proved that the 2-dimensional Weisfeiler-Leman algorithm implicitly computes the decomposition of a graph into its 3-connected components and insights are obtained about the connectivity of constituent graphs of association schemes. Expand

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