Lax Lean Archive

Independent Set without a 5×5 induced grid minor

Lax762056.IndependentSetHardness · concepts/Lax762056/IndependentSetHardness.lean · lax-762056

proven

Loading review…

Community review

Flags

Each flag is tied to a public ORCID identity and explains why this concept may be incorrect.

No flags have been submitted.

    Community review

    Flag this concept

    State precisely what appears incorrect. This explanation will be public under your ORCID name.

    No source line selected.

    Natural Language Statement

    Theorem

    Deciding whether a graph has an independent set of size at least kk is NP-hard even when the graph excludes the 5×55\times5 grid as an induced minor. Consequently, Maximum Independent Set is NP-hard on this class.

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

    Each proof establishes this claim relative to its assumptions.

    In the paper

    • page 2 of this submission's paper
    • page 3 of this submission's paper

    Lean source view on GitHub

    1import Lax762056.Grid
    2import Lax762056.GraphProblems
    3
    4/-!
    5---
    6title: Independent Set without a 5×5 induced grid minor
    7type: theorem
    8---
    9Deciding whether a graph has an independent set of size at least kk is
    10NP-hard even when the graph excludes the 5×55\times5 grid as an induced minor.
    11Consequently, Maximum Independent Set is NP-hard on this class.
    12-/
    13
    14namespace Lax762056.IndependentSetHardness
    15
    16open GraphProblems Grid
    17
    18axiom independentSet_inducedGrid_hardness :
    19 NPHardOn IndependentSet (ExcludesInducedGrid 5)
    20
    21end Lax762056.IndependentSetHardness
    22
    Show Proof
    Builds on
    Used by

    none

    From Mathlib

    none

    Discussion

    Ask a question or add context. Endorsements and structured flags are kept in the review panel above.

    Loading discussion…