Lax Lean Archive

Treewidth monotonicity under graph minors

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

proven

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    Natural Language Statement

    Theorem

    Taking a graph minor cannot increase treewidth.

    Concept map
    3 concepts
    100%
    Proven claimDefinitionThis conceptRelated conceptA → B: B builds on A
    Evidence

    Each proof establishes this claim relative to its assumptions.

    Lean source view on GitHub

    1import Lax17.Minor
    2import Lax17.Treewidth
    3
    4/-!
    5---
    6title: Treewidth monotonicity under graph minors
    7type: theorem
    8---
    9Taking a graph minor cannot increase treewidth.
    10-/
    11
    12namespace Lax17.TreewidthMinorMonotonicity
    13
    14universe u
    15
    16/-- Taking a graph minor cannot increase treewidth. -/
    17axiom treewidth_mono_minor :
    18 ∀ {V W : Type u} [Fintype V] [DecidableEq V]
    19 [Fintype W] [DecidableEq W]
    20 (G : SimpleGraph V) (H : SimpleGraph W),
    21 Lax17.Minor.IsMinor H G →
    22 Lax17.Treewidth.treewidth H ≤ Lax17.Treewidth.treewidth G
    23
    24end Lax17.TreewidthMinorMonotonicity
    25
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