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Linear Neighbourhood Complexity of Bounded Merge-Width Classes

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

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    Natural Language Statement

    Theorem

    Every class of finite simple graphs with bounded merge-width has linear neighbourhood complexity.

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    3 concepts
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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.MergeWidth
    2import Lax9.NeighborhoodComplexity
    3
    4/-!
    5---
    6title: Linear Neighbourhood Complexity of Bounded Merge-Width Classes
    7type: theorem
    8---
    9Every class of finite simple graphs with bounded merge-width has linear
    10neighbourhood complexity.
    11-/
    12
    13namespace Lax9.BoundedMergeWidthLinearNeighborhoodComplexity
    14
    15open Lax9.MergeWidth
    16open Lax9.NeighborhoodComplexity
    17
    18/-- Every graph class of bounded merge-width has linear neighbourhood
    19complexity. -/
    20axiom bounded_mergeWidth_linearNeighborhoodComplexity
    21 (C : GraphClass) (h : BoundedMergeWidth C) : LinearNeighborhoodComplexity C
    22
    23end Lax9.BoundedMergeWidthLinearNeighborhoodComplexity
    24
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