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The Weisfeiler-Leman Algorithm and Recognition of Graph Properties

  • 2021
  • OriginalPaper
  • Chapter
Published in:
Authors
Frank Fuhlbrück
Johannes Köbler
Ilia Ponomarenko
Oleg Verbitsky
Published in
Algorithms and Complexity
Publisher
Springer International Publishing

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Abstract

The chapter delves into the Weisfeiler-Leman algorithm, particularly its k-dimensional version, and its significant role in graph isomorphism testing. It highlights the algorithm's limitations, such as its inability to distinguish certain non-isomorphic graphs despite its high dimension. The text introduces a new combinatorial approach to recognize vertex-transitivity in graphs with a prime number of vertices, showcasing its conceptual simplicity and efficiency. Additionally, it explores lower bounds for the algorithm's dimension and discusses the implications of its limitations on recognizing graph properties. The chapter concludes with a discussion of potential extensions and open questions in the field.
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This summary of the content was generated with the help of AI.

O. Verbitsky was supported by DFG grant KO 1053/8-1. He is on leave from the IAPMM, Lviv, Ukraine.

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previous chapter A Multistage View on 2-Satisfiability
next chapter The Parameterized Suffix Tray
Title
The Weisfeiler-Leman Algorithm and Recognition of Graph Properties
Authors
Frank Fuhlbrück
Johannes Köbler
Ilia Ponomarenko
Oleg Verbitsky
Copyright Year
2021
Book
Algorithms and Complexity

Print ISBN: 978-3-030-75241-5

Electronic ISBN: 978-3-030-75242-2

Copyright Year: 2021

DOI
https://doi.org/10.1007/978-3-030-75242-2_17
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