Lax Lean Archive

Trees are outerplanar

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

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    Natural Language Statement

    Theorem

    Every finite tree is outerplanar.

    The proof excludes K4K₄ and K2,3K₂,₃ using preservation of acyclicity under minors. It depends on the excluded-minor characterization of outerplanarity, which remains open in this submission.

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    Proven claimDefinitionThis conceptRelated conceptA → B: B builds on A
    Evidence

    Each proof establishes this claim relative to its assumptions.

    Lean source view on GitHub

    1import Lax68.Trees
    2import Lax68.Outerplanar
    3
    4/-!
    5---
    6title: Trees are outerplanar
    7type: theorem
    8---
    9Every finite tree is outerplanar.
    10
    11The proof excludes `K₄` and `K₂,₃` using preservation of acyclicity under
    12minors. It depends on the excluded-minor characterization of outerplanarity,
    13which remains open in this submission.
    14-/
    15
    16set_option autoImplicit false
    17
    18namespace Lax68.TreeOuterplanar
    19
    20/-- Every finite tree is outerplanar. -/
    21axiom tree_outerplanar {V : Type*} [Finite V] {G : SimpleGraph V} :
    22 Lax68.Trees.IsTree G →
    23 Lax68.Outerplanar.IsOuterplanar G
    24
    25end Lax68.TreeOuterplanar
    26
    Show Proof 1Show Proof 2
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