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Lax17.GridMinor

Square grid minors

concepts/Lax17/GridMinor.lean · lax-17

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    Definition

    A graph contains a square grid minor of order gg when the canonical g×gg\times g square grid is a minor of it.

    Because graph-minor containment is invariant under relabelling, choosing the canonical coordinate grid loses no generality.

    Lean source view on GitHub

    1import Lax17.Grid
    2import Lax17.Minor
    3
    4/-!
    5---
    6title: Square grid minors
    7type: definition
    8---
    9A graph contains a square grid minor of order \(g\) when the canonical
    10\(g\times g\) square grid is a minor of it.
    11
    12Because graph-minor containment is invariant under relabelling, choosing the
    13canonical coordinate grid loses no generality.
    14-/
    15
    16namespace Lax17.GridMinor
    17
    18universe u
    19
    20/-- `G` contains the `g × g` square grid as a minor. -/
    21def ContainsGridMinor {V : Type u} (G : SimpleGraph V) (g : ℕ) : Prop :=
    22 Lax17.Minor.IsMinor (Lax17.Grid.squareGrid g) G
    23
    24end Lax17.GridMinor
    25

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