Lax Lean Archive

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

lax-9·formalized by Édouard Bonnet·registered·created ·GitHub @5169406·Lean v4.33.0 epoch · mathlib db584cd6d46c

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    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.

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    @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/},
}

    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

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