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Clique minors from connected matchings

Lax342547.MatchingMinorBound · concepts/Lax342547/MatchingMinorBound.lean · lax-342547

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    Natural Language Statement

    Theorem

    Every finite graph satisfies 3h(G)≤∣V(G)∣+4cm(G)+23h(G)\le |V(G)|+4\mathrm{cm}(G)+2. This is Proposition 3.5 of the source paper, written with integer coefficients.

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

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    Lean source view on GitHub

    1import Lax342547.ConnectedMatching
    2import Lax342547.CliqueMinor
    3
    4/-!
    5---
    6title: Clique minors from connected matchings
    7type: theorem
    8---
    9Every finite graph satisfies 3h(G)≤∣V(G)∣+4cm(G)+23h(G)\le |V(G)|+4\mathrm{cm}(G)+2.
    10This is Proposition 3.5 of the source paper, written with integer coefficients.
    11-/
    12
    13namespace Lax342547.MatchingMinorBound
    14
    15open ConnectedMatching CliqueMinor
    16
    17axiom hadwiger_matching_bound {V : Type} [Fintype V] (G : SimpleGraph V) :
    18 3 * hadwigerNumber G ≤ Fintype.card V + 4 * connectedMatchingNumber G + 2
    19
    20end Lax342547.MatchingMinorBound
    21
    Show Proof
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