# Recent Advances on the Graph Isomorphism Problem

@article{Grohe2020RecentAO, title={Recent Advances on the Graph Isomorphism Problem}, author={Martin Grohe and Daniel Neuen}, journal={ArXiv}, year={2020}, volume={abs/2011.01366} }

We give an overview of recent advances on the graph isomorphism problem. Our main focus will be on Babai's quasi-polynomial time isomorphism test and subsequent developments that led to the design of isomorphism 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. A second focus will be the combinatorial Weisfeiler-Leman algorithm.

## 12 Citations

### Isomorphism Testing for Graphs Excluding Small Topological Subgraphs

- MathematicsSODA
- 2022

We give an isomorphism test that runs in time $n^{\operatorname{polylog}(h)}$ on all $n$-vertex graphs excluding some $h$-vertex vertex graph as a topological subgraph. Previous results state that…

### On WL-Rank and WL-Dimension of Some Deza Circulant Graphs

- MathematicsGraphs and Combinatorics
- 2021

It is proved that some families of Deza circulant graphs have WL-rank 5 or 6 and WL -dimension at most 3.

### Description Graphs, Matrix-Power Stabilizations and Graph Isomorphism in Polynomial Time

- MathematicsArXiv
- 2022

. It is conﬁrmed in this work that the graph isomorphism can be tested in polynomial time, which resolves a longstanding problem in the theory of computation. The contributions are in three phases as…

### Theory research in India

- Computer ScienceCommun. ACM
- 2022

The last few years has been a productive period for research in the field of computational complexity in India, and some of the exciting results include constant factor approximation algorithm for finding a maximum independent set of rectangles, improved bounds for perfect sampling of k-coloring in graphs, an optimal FPT-approximation scheme for k-way cut, and a new online algorithm for caching.

### Defining Cases and Variants for Object-Centric Event Data

- Computer Science2022 4th International Conference on Process Mining (ICPM)
- 2022

The case concept for object-centric process mining is introduced: process executions, which are graph-based generalizations of cases as considered in traditional process mining and determine equivalent process behavior with respect to an attribute using graph isomorphism.

### Fixed-parameter tractability of graph isomorphism in graphs with an excluded minor

- MathematicsSTOC
- 2022

We prove that Graph Isomorphism and Canonization in graphs excluding a fixed graph H as a minor can be solved by an algorithm working in time f(H)· nO(1), where f is some function. In other words, we…

### On pseudofrobenius imprimitive association schemes

- MathematicsJournal of Algebraic Combinatorics
- 2022

An (association) scheme is said to be Frobenius if it is the scheme of a Frobenius group. A scheme which has the same tensor of intersection numbers as some Frobenius scheme is said to be…

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

- Education, Computer ScienceArXiv
- 2021

A comprehensive overview of the Weisfeiler–Leman algorithm’s use in a machine-learning setting, focusing on the supervised regime, and discusses the theoretical background, how to use it for supervised graph and node representation learning, and recent extensions.

### Reconstruction for Powerful Graph Representations

- Computer ScienceNeurIPS
- 2021

This work shows the extent to which graph reconstruction—reconstructing a graph from its subgraphs—can mitigate the theoretical and practical problems currently faced by GRL architectures and demonstrates how it boosts state-of-the-art GNN’s performance across nine real-world benchmark datasets.

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We prove that there is a graph isomorphism test running in time $n^{\text{polylog}(h)}$ on $n$-vertex graphs excluding some h-vertex graph as a minor. Previously known bounds were…

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