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Lax68.Outerplanar

Outerplanar graphs

concepts/Lax68/Outerplanar.lean · lax-68

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    Definition

    A graph is outerplanar here when it has a crossing-free straight-line drawing with every vertex on one circle, a compact certificate for having every vertex on the boundary of the outer face.

    Lean source view on GitHub

    1import Lax68.StraightLineDrawings
    2
    3/-!
    4---
    5title: Outerplanar graphs
    6type: definition
    7---
    8A graph is outerplanar here when it has a crossing-free straight-line drawing
    9with every vertex on one circle, a compact certificate for having every
    10vertex on the boundary of the outer face.
    11-/
    12
    13set_option autoImplicit false
    14
    15namespace Lax68.Outerplanar
    16
    17structure OuterplaneDrawing {V : Type*} (G : SimpleGraph V)
    18 extends StraightLineDrawings.StraightLineDrawing G where
    19 radius : ℝ
    20 radius_pos : 0 < radius
    21 onBoundary :
    22 ∀ v : V,
    23 let p := toStraightLineDrawing.point v
    24 p.1 ^ 2 + p.2 ^ 2 = radius ^ 2
    25
    26def IsOuterplanar {V : Type*} (G : SimpleGraph V) : Prop :=
    27 Nonempty (OuterplaneDrawing G)
    28
    29end Lax68.Outerplanar
    30

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