Lax Lean Archive

Draft — mutable and not usable as a dependency; its citation marks the draft state.

χ-Boundedness and Neighbourhood Complexity of Bounded Merge-Width Graphs

lax-9·formalized by Édouard Bonnet·created 2026-08-02·GitHub @cb4d609·Lean v4.30.0 epoch · mathlib c5ea00351c28

Loading review…

Community review

Flags

Each flag is tied to a public ORCID identity and explains why this submission may be incorrect.

No flags have been submitted.

    Community review

    Flag this submission

    State precisely what appears incorrect. This explanation will be public under your ORCID name.

    Abstract

    This submission formalizes two results of Marthe Bonamy and Colin Geniet: every graph class of bounded merge-width is χ-bounded, and every such class has linear neighbourhood complexity, Theorems 1.2 and 1.5 of χ-Boundedness and Neighbourhood Complexity of Bounded Merge-Width Graphs (https://arxiv.org/abs/2504.08266). In particular, merge sequences, radius-rr merge-width, χ-boundedness, and neighbourhood complexity are defined in Lean.

    Concepts

    thm✓proven claimdefdefinition

    Concept map

    Proven claimDefinitionThis submissionA → B: B builds on A

    Proofs

    Proof networkview on GitHub

    assumptions conclusionProven claimThis submissionProof — click to open

    Lean sources for these proofs: proofs/ on GitHub

    Proof code is not displayed; the archive records each proof's checked relationship between claims.

    Related submissions

    No other submission in the archive builds on this one, and this one builds on none.

    Cite this

    @misc{lax-9,
  author = {Édouard Bonnet},
  title = {χ-Boundedness and Neighbourhood Complexity of Bounded Merge-Width Graphs},
  year = {2026},
  howpublished = {Lax Archive, lax-9},
  url = {https://laxarchive.org/lax-9/},
  note = {draft},
}

    References

    1. Marthe Bonamy and Colin Geniet. χ-Boundedness and Neighbourhood Complexity of Bounded Merge-Width Graphs. 2025. doi:10.48550/arXiv.2504.08266 · arXiv:2504.08266

    Community review

    Discussion

    Ask a question or add context. Endorsements and structured flags are kept in the review panel above; your ORCID profile must share a public name.

    0 comments

    Loading discussion…