Lax Lean Archive

Induced grid exclusion in the reduction

Lax222097.GridExclusion · concepts/Lax222097/GridExclusion.lean · lax-222097

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    Natural Language Statement

    Lemma

    For every finite simple graph FF, the reduction graph GFG_F excludes the 5×55\times5 grid as an induced minor.

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

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    In the paper

    • page 5 of this submission's paper

    Lean source view on GitHub

    1import Lax222097.Reduction
    2import Lax222097.Grid
    3
    4/-!
    5---
    6title: Induced grid exclusion in the reduction
    7type: lemma
    8---
    9For every finite simple graph FF, the reduction graph GFG_F excludes
    10the 5×55\times5 grid as an induced minor.
    11-/
    12
    13namespace Lax222097.GridExclusion
    14
    15open Grid Reduction
    16
    17axiom reduction_excludes_inducedGrid {n : ℕ} (F : SimpleGraph (Fin n)) :
    18 ExcludesInducedGrid 5 (reductionGraph F)
    19
    20end Lax222097.GridExclusion
    21
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