Lax Lean Archive

Draft — mutable and not usable as a dependency; its citation marks the draft state.

Lax68.KuratowskiPlanarity

Kuratowski's theorem in straight-line form

concepts/Lax68/KuratowskiPlanarity.lean · lax-68

open

Loading review…

Community review

Flags

Each flag is tied to a public ORCID identity and explains why this concept may be incorrect.

No flags have been submitted.

    Community review

    Flag this concept

    State precisely what appears incorrect. This explanation will be public under your ORCID name.

    No source line selected.

    Concept map

    Open claimDefinitionThis conceptRelated conceptA → B: B builds on A

    Evidence

    Each proof establishes this claim relative to its assumptions.

    No proof in the archive yet — this claim is open.

    Theorem

    A finite simple graph admits a crossing-free straight-line drawing exactly when it contains no subdivision of K₅ or K₃,₃. This is Kuratowski's theorem together with Fáry's straight-line drawing theorem.

    Lean source view on GitHub

    1import Lax68.GraphTopologicalMinors
    2import Lax68.Planar
    3
    4/-!
    5---
    6title: Kuratowski's theorem in straight-line form
    7type: theorem
    8---
    9A finite simple graph admits a crossing-free straight-line drawing exactly
    10when it contains no subdivision of *K₅* or *K₃,₃*. This is Kuratowski's
    11theorem together with Fáry's straight-line drawing theorem.
    12-/
    13
    14set_option autoImplicit false
    15
    16namespace Lax68.KuratowskiPlanarity
    17
    18axiom planar_iff_kuratowskiFree
    19 {V : Type*} {G : SimpleGraph V} :
    20 Finite V →
    21 (Lax68.Planar.IsPlanar G ↔
    22 Lax68.GraphTopologicalMinors.IsKuratowskiFree G)
    23
    24end Lax68.KuratowskiPlanarity
    25

    Builds on

    Used by

    none

    From Mathlib

    none

    Community review

    Discussion

    Ask a question or add context. Endorsements and structured flags are kept in the review panel above; your ORCID profile must share a public name.

    0 comments

    Loading discussion…