# Logarithmic Weisfeiler-Leman Identifies All Planar Graphs

@inproceedings{Grohe2021LogarithmicWI, title={Logarithmic Weisfeiler-Leman Identifies All Planar Graphs}, author={Martin Grohe and Sandra Kiefer}, booktitle={ICALP}, year={2021} }

The Weisfeiler-Leman (WL) algorithm is a well-known combinatorial procedure for detecting symmetries in graphs and it is widely used in graph-isomorphism tests. It proceeds by iteratively refining a colouring of vertex tuples. The number of iterations needed to obtain the final output is crucial for the parallelisability of the algorithm. We show that there is a constant k such that every planar graph can be identified (that is, distinguished from every non-isomorphic graph) by the k…

## 6 Citations

### A Study of Weisfeiler-Leman Colorings on Planar Graphs

- Mathematics, Computer ScienceICALP
- 2022

The colorings computed by 2-WL on planar graphs, a combinatorial procedure that computes colorings on graphs, are investigated and the graphs induced by edge color classes in the graph are analyzed.

### Combinatorial refinement on circulant graphs

- MathematicsArXiv
- 2022

The combinatorial reﬁnement techniques have proven to be an eﬃcient approach to isomorphism testing for particular classes of graphs. If the number of reﬁnement rounds is small, this puts the…

### On the Parallel Complexity of Group Isomorphism and Canonization via Weisfeiler–Leman

- Mathematics
- 2022

In this paper, we show that the constant-dimensional Weisfeiler–Leman algorithm for groups (Brachter & Schweitzer, LICS 2020) can be fruitfully used to improve parallel complexity upper bounds on…

### On the parallel complexity of Group Isomorphism via Weisfeiler-Leman

- Mathematics
- 2021

In this paper, we show that the constant-dimensional Weisfeiler–Leman algorithm for groups (Brachter & Schweitzer, LICS 2020) can be fruitfully used to improve parallel complexity upper bounds on…

### Weisfeiler and Leman go Machine Learning: The Story so far

- Education, Computer ScienceArXiv
- 2021

This research presents a parallel version of the TSP called TSP “TSP2” that was developed at the proofs stage at the University of California, Berkeley with real-time constraints.

### On the Descriptive Complexity of Groups without Abelian Normal Subgroups

- Mathematics
- 2022

In this paper, we explore the descriptive complexity theory of ﬁnite groups by examining the power of the second Ehrenfeucht–Fra¨ıss´e bijective pebble game in Hella’s ( Ann. Pure Appl. Log. , 1989)…

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