Lax Lean Archive

The excluded-minor characterization of outerplanarity

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

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    Natural Language Statement

    Opn

    For every finite simple graph, having an outerplane drawing is equivalent to containing neither K₄ nor K₂,₃ as a minor.

    This is the standard excluded-minor characterization of outerplanar graphs. It is an open theorem in this submission.

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    Proven claimDefinitionThis conceptRelated conceptA → B: B builds on A
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    1import Lax68.Outerplanar
    2
    3/-!
    4---
    5title: The excluded-minor characterization of outerplanarity
    6type: opn
    7---
    8For every finite simple graph, having an outerplane drawing is equivalent to
    9containing neither *K₄* nor *K₂,₃* as a minor.
    10
    11This is the standard excluded-minor characterization of outerplanar graphs.
    12It is an open theorem in this submission.
    13-/
    14
    15set_option autoImplicit false
    16
    17namespace Lax68.OuterplanarExcludedMinors
    18
    19/-- A finite graph is outerplanar exactly when it has neither `K₄` nor `K₂,₃`
    20as a minor. This remains open in the present formalization. -/
    21axiom outerplanar_iff_excludedMinors
    22 {V : Type*} {G : SimpleGraph V} :
    23 Finite V →
    24 (Lax68.Outerplanar.IsOuterplanar G ↔
    25 Lax68.Outerplanar.IsOuterplanarByExcludedMinors G)
    26
    27end Lax68.OuterplanarExcludedMinors
    28
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