Triangulations
Lax68.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.
Concept map
In the paper
- page 2 of the paper of lax-326031, Graph Classes and Width Parameters
- page 3 of the paper of lax-326031, Graph Classes and Width Parameters
Lean source view on GitHub
| 1 | import Lax68.Planar |
| 2 | |
| 3 | /-! |
| 4 | --- |
| 5 | title: Triangulations |
| 6 | type: definition |
| 7 | --- |
| 8 | |
| 9 |  |
| 10 | |
| 11 | A triangulation of a graph G is a planar supergraph T on the same vertex set, |
| 12 | with at least three vertices, to which no edge can be added while preserving |
| 13 | planarity. For a plane embedding this is equivalent to every face of T being |
| 14 | bounded by a triangle. |
| 15 | -/ |
| 16 | |
| 17 | set_option autoImplicit false |
| 18 | |
| 19 | namespace Lax68.Triangulations |
| 20 | |
| 21 | def IsTriangulationOf {V : Type*} |
| 22 | (G T : SimpleGraph V) : Prop := |
| 23 | (∃ a b c : V, a ≠ b ∧ a ≠ c ∧ b ≠ c) ∧ |
| 24 | G ≤ T ∧ |
| 25 | Planar.IsPlanar T ∧ |
| 26 | ∀ H : SimpleGraph V, |
| 27 | T < H → |
| 28 | ¬ Planar.IsPlanar H |
| 29 | |
| 30 | end Lax68.Triangulations |
| 31 |
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