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Feedback vertex number is at most feedback edge number

Lax379983.FeedbackNumberComparison · concepts/Lax379983/FeedbackNumberComparison.lean · lax-379983

proven

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    Natural Language Statement

    Theorem

    For every finite undirected simple graph GG,

    FVN⁡(G)≤FEN⁡(G).\operatorname{FVN}(G)\leq\operatorname{FEN}(G).

    No connectedness or nonemptiness assumption is required.

    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 Lax379983.FeedbackVertexNumber
    2import Lax379983.FeedbackEdgeNumber
    3
    4/-!
    5---
    6title: Feedback vertex number is at most feedback edge number
    7type: theorem
    8---
    9For every finite undirected simple graph GG,
    10
    11FVN⁡(G)≤FEN⁡(G).\operatorname{FVN}(G)\leq\operatorname{FEN}(G).
    12
    13No connectedness or nonemptiness assumption is required.
    14-/
    15
    16namespace Lax379983.FeedbackNumberComparison
    17
    18open Lax379983.FeedbackVertexNumber Lax379983.FeedbackEdgeNumber
    19
    20/-- Every finite simple graph has feedback vertex number at most its feedback edge number. -/
    21axiom feedbackVertexNumber_le_feedbackEdgeNumber {V : Type*} [Finite V]
    22 (G : SimpleGraph V) : feedbackVertexNumber G ≤ feedbackEdgeNumber G
    23
    24end Lax379983.FeedbackNumberComparison
    25
    Show Proof
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