Lax Lean Archive

Wagner's theorem

Lax68.PlanarExcludedMinors · concepts/Lax68/PlanarExcludedMinors.lean · lax-68

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    Natural Language Statement

    Opn

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

    This statement is open in this submission.

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    4 concepts
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    Open claimDefinitionThis conceptRelated conceptA → B: B builds on A
    Evidence

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    Lean source view on GitHub

    1import Lax68.Planar
    2
    3/-!
    4---
    5title: Wagner's theorem
    6type: opn
    7---
    8For every finite simple graph, admitting a crossing-free drawing is equivalent
    9to containing neither *K₅* nor *K₃,₃* as a minor.
    10
    11This statement is open in this submission.
    12-/
    13
    14set_option autoImplicit false
    15
    16namespace Lax68.PlanarExcludedMinors
    17
    18axiom planar_iff_excludedMinors
    19 {V : Type*} {G : SimpleGraph V} :
    20 Finite V →
    21 (Lax68.Planar.IsPlanar G ↔
    22 Lax68.Planar.IsPlanarByExcludedMinors G)
    23
    24end Lax68.PlanarExcludedMinors
    25
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