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Lax68.WagnerObstructionBridge

The Kuratowski-Wagner obstruction bridge

concepts/Lax68/WagnerObstructionBridge.lean · lax-68

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    Open claimDefinitionThis conceptRelated conceptA → B: B builds on A

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    Theorem

    A graph contains a subdivision of K₅ or K₃,₃ exactly when it contains K₅ or K₃,₃ as a minor. This special equivalence does not hold for arbitrary forbidden graphs.

    Lean source view on GitHub

    1import Lax68.GraphTopologicalMinors
    2import Lax68.Planar
    3
    4/-!
    5---
    6title: The Kuratowski-Wagner obstruction bridge
    7type: theorem
    8---
    9A graph contains a subdivision of *K₅* or *K₃,₃* exactly when it contains
    10*K₅* or *K₃,₃* as a minor. This special equivalence does not hold for
    11arbitrary forbidden graphs.
    12-/
    13
    14set_option autoImplicit false
    15
    16namespace Lax68.WagnerObstructionBridge
    17
    18axiom kuratowskiFree_iff_excludedMinors
    19 {V : Type*} {G : SimpleGraph V} :
    20 Lax68.GraphTopologicalMinors.IsKuratowskiFree G ↔
    21 Lax68.Planar.IsPlanarByExcludedMinors G
    22
    23end Lax68.WagnerObstructionBridge
    24

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