Lax Lean Archive

Mader's admissible split-off theorem

Lax17.Mader · concepts/Lax17/Mader.lean · lax-17

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    Natural Language Statement

    Theorem

    Every eligible splitting centre has a pair of incident edges whose split-off preserves the relevant local edge-connectivities.

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

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    1import Lax17.TerminalConnectivity
    2
    3/-!
    4---
    5title: Mader's admissible split-off theorem
    6type: theorem
    7---
    8Every eligible splitting centre has a pair of incident edges whose split-off
    9preserves the relevant local edge-connectivities.
    10-/
    11
    12namespace Lax17.Mader
    13
    14universe u
    15
    16/-- Mader's admissible split-off theorem, including the exceptional
    17degree-three exclusion. -/
    18axiom maderAdmissibleSplitOff :
    19 ∀ {V : Type u} [Fintype V] [DecidableEq V]
    20 (H : Lax17.TerminalConnectivity.EdgeIndexedGraph V) (s : V),
    21 2 ≤ H.degree s → H.degree s ≠ 3 → H.NoIncidentCutEdge s →
    22 ∃ p : H.SplitPair s, H.IsMaderAdmissible p
    23
    24end Lax17.Mader
    25
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