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Lax68.PlanarExcludedMinors

Wagner's theorem

concepts/Lax68/PlanarExcludedMinors.lean · lax-68

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    Theorem

    For every finite simple graph, admitting a crossing-free drawing is equivalent to containing neither K₅ nor K₃,₃ as a minor.

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    1import Lax68.Planar
    2
    3/-!
    4---
    5title: Wagner's theorem
    6type: theorem
    7---
    8For every finite simple graph, admitting a crossing-free drawing is equivalent
    9to containing neither *K₅* nor *K₃,₃* as a minor.
    10-/
    11
    12set_option autoImplicit false
    13
    14namespace Lax68.PlanarExcludedMinors
    15
    16axiom planar_iff_excludedMinors
    17 {V : Type*} {G : SimpleGraph V} :
    18 Finite V →
    19 (Lax68.Planar.IsPlanar G ↔
    20 Lax68.Planar.IsPlanarByExcludedMinors G)
    21
    22end Lax68.PlanarExcludedMinors
    23
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