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The Weisfeiler–Leman Dimension of Chordal Bipartite Graphs Without Bipartite Claw

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Abstract

A graph X is said to be chordal bipartite if it is bipartite and contains no induced cycle of length at least 6. It is proved that if X does not contain bipartite claw as an induced subgraph, then the Weisfeiler–Leman dimension of X is at most 3. This implies that the Weisfeiler–Leman dimension of any bipartite permutation graph is at most 3. The proof is based on the theory of coherent configurations.

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Notes

  1. This closure is nothing else than the \(\alpha \)-extension of the coherent configuration \({{\,{\mathrm{WL}}\,}}(X)\), see [5, Definition 3.3.1].

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Authors and Affiliations

  1. St. Petersburg Department of the Steklov Mathematical Institute, St.Petersburg, Russia

    Ilia Ponomarenko

  2. Sobolev Institute of Mathematics, Novosibirsk, Russia

    Grigory Ryabov

  3. Novosibirsk State University, Novosibirsk, Russia

    Grigory Ryabov

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  1. Ilia Ponomarenko
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  2. Grigory Ryabov
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Correspondence to Grigory Ryabov.

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The work is supported by the Russian Foundation for Basic Research (Project 18-01-00752).

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Ponomarenko, I., Ryabov, G. The Weisfeiler–Leman Dimension of Chordal Bipartite Graphs Without Bipartite Claw. Graphs and Combinatorics 37, 1089–1102 (2021). https://doi.org/10.1007/s00373-021-02308-7

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  • DOI: https://doi.org/10.1007/s00373-021-02308-7

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