Lax Lean Archive

χ-Boundedness of Bounded Merge-Width Classes

Lax9.BoundedMergeWidthChiBounded · concepts/Lax9/BoundedMergeWidthChiBounded.lean · lax-9

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    Natural Language Statement

    Theorem

    Every class of finite simple graphs with bounded merge-width is χ-bounded.

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    Proven claimDefinitionThis conceptRelated conceptA → B: B builds on A
    Evidence

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    Lean source view on GitHub

    1import Lax9.ChiBoundedness
    2import Lax9.MergeWidth
    3
    4/-!
    5---
    6title: χ-Boundedness of Bounded Merge-Width Classes
    7type: theorem
    8---
    9Every class of finite simple graphs with bounded merge-width is χ-bounded.
    10-/
    11
    12namespace Lax9.BoundedMergeWidthChiBounded
    13
    14open Lax9.ChiBoundedness
    15open Lax9.MergeWidth
    16
    17/-- Every graph class of bounded merge-width is χ-bounded. -/
    18axiom bounded_mergeWidth_chiBounded
    19 (C : GraphClass) (h : BoundedMergeWidth C) : ChiBounded C
    20
    21end Lax9.BoundedMergeWidthChiBounded
    22
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