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Lax68.Triangulations

Triangulations

concepts/Lax68/Triangulations.lean · lax-68

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    Definition

    A triangulation of a graph G is a planar supergraph T on the same vertex set, with at least three vertices, to which no edge can be added while preserving planarity. For a plane embedding this is equivalent to every face of T being bounded by a triangle.

    Lean source view on GitHub

    1import Lax68.Planar
    2
    3/-!
    4---
    5title: Triangulations
    6type: definition
    7---
    8A triangulation of a graph G is a planar supergraph T on the same vertex set,
    9with at least three vertices, to which no edge can be added while preserving
    10planarity. For a plane embedding this is equivalent to every face of T being
    11bounded by a triangle.
    12-/
    13
    14set_option autoImplicit false
    15
    16namespace Lax68.Triangulations
    17
    18def IsTriangulationOf {V : Type*}
    19 (G T : SimpleGraph V) : Prop :=
    20 (∃ a b c : V, a ≠ b ∧ a ≠ c ∧ b ≠ c) ∧
    21 G ≤ T ∧
    22 Planar.IsPlanar T ∧
    23 ∀ H : SimpleGraph V,
    24 T < H →
    25 ¬ Planar.IsPlanar H
    26
    27end Lax68.Triangulations
    28

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