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Minors of acyclic graphs are acyclic

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

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    Natural Language Statement

    Theorem

    Every minor of an acyclic graph is acyclic. Consequently, a graph containing a cycle cannot be a minor of a tree.

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

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    Lean source view on GitHub

    1import Mathlib.Combinatorics.SimpleGraph.Acyclic
    2import Lax68.GraphMinors
    3
    4/-!
    5---
    6title: Minors of acyclic graphs are acyclic
    7type: theorem
    8---
    9Every minor of an acyclic graph is acyclic. Consequently, a graph containing
    10a cycle cannot be a minor of a tree.
    11-/
    12
    13set_option autoImplicit false
    14
    15namespace Lax68.AcyclicMinors
    16
    17/-- Taking a graph minor preserves acyclicity. -/
    18axiom acyclic_minor {V W : Type*} {G : SimpleGraph V} {H : SimpleGraph W} :
    19 G.IsAcyclic → Lax68.GraphMinors.IsMinor H G → H.IsAcyclic
    20
    21end Lax68.AcyclicMinors
    22
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