Lax Lean Archive

Paths

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

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    Natural Language Statement

    Definition

    Path graph illustration
    Path graph illustration

    A finite path graph is a graph isomorphic to the standard path graph on a positive number of vertices.

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    Proven claimDefinitionThis conceptRelated conceptA → B: B builds on A

    In the paper

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    1import Mathlib.Combinatorics.SimpleGraph.Hasse
    2
    3/-!
    4---
    5title: Paths
    6type: definition
    7---
    8
    9![Path graph illustration](https://raw.githubusercontent.com/lax-archive/lax-submissions/4dd917c8b9a1e181ec951b7f6fa384262af31fa9/planar-graph-classes-v4-33/assets/path.svg "Path graph illustration")
    10
    11A finite path graph is a graph isomorphic to the standard path graph on a
    12positive number of vertices.
    13-/
    14
    15set_option autoImplicit false
    16
    17namespace Lax68.Paths
    18
    19def HasPathShape {V : Type*} (G : SimpleGraph V) : Prop :=
    20 ∃ n : ℕ,
    21 0 < n ∧
    22 Nonempty (G ≃g SimpleGraph.pathGraph n)
    23
    24def IsPath {V : Type*} (G : SimpleGraph V) : Prop :=
    25 HasPathShape G
    26
    27end Lax68.Paths
    28
    Builds on

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    Used by
    From Mathlib

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