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Graphs without a 3-connected subgraph are 4-colorable

Lax10.FragileFourColorable · concepts/Lax10/FragileFourColorable.lean · lax-10

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    Natural Language Statement

    Theorem

    Every finite simple graph with no 33-connected subgraph is 44-colorable.

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    Proven claimDefinitionThis conceptRelated conceptA → B: B builds on A
    Evidence

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    1import Lax10.Fragile
    2
    3/-!
    4---
    5title: Graphs without a 3-connected subgraph are 4-colorable
    6type: theorem
    7---
    8Every finite simple graph with no 33-connected subgraph is 44-colorable.
    9-/
    10
    11namespace Lax10.FragileFourColorable
    12
    13universe u
    14
    15open Lax10.ThreeConnectedAndColorable
    16open Lax10.Fragile
    17
    18/-- Every finite simple graph with no 33-connected subgraph is 44-colorable. -/
    19axiom fragile_four_colorable {V : Type u} [Fintype V] [DecidableEq V]
    20 (G : SimpleGraph V) (hfragile : HasNoThreeConnectedSubgraph G) :
    21 KColorable 4 G
    22
    23end Lax10.FragileFourColorable
    24
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