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Six color theorem

Lax909950.SixColoring · concepts/Lax909950/SixColoring.lean · lax-909950

proven

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    Natural Language Statement

    Theorem

    Every finite planar graph admits a proper coloring of its vertices with six colors, i.e. an assignment of one of six colors to each vertex such that adjacent vertices receive different colors.

    Concept map
    4 concepts
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    Proven claimDefinitionThis conceptRelated conceptA → B: B builds on A
    Evidence

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    In the paper

    • page 2 of this submission's paper

    Lean source view on GitHub

    1import Mathlib.Combinatorics.SimpleGraph.Coloring.Vertex
    2import Lax68.Planar
    3
    4/-!
    5---
    6title: Six color theorem
    7type: theorem
    8---
    9Every finite planar graph admits a proper coloring of its vertices with six
    10colors, i.e. an assignment of one of six colors to each vertex such that
    11adjacent vertices receive different colors.
    12-/
    13
    14set_option autoImplicit false
    15
    16namespace Lax909950.SixColoring
    17
    18/-- Every finite planar graph is 66-colorable. -/
    19axiom six_colorable {V : Type*} [Finite V] {G : SimpleGraph V}
    20 (hG : Lax68.Planar.IsPlanar G) :
    21 G.Colorable 6
    22
    23end Lax909950.SixColoring
    24
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