Lax Lean Archive

Graph crawling is NP-complete

Lax117614.GraphCrawlingNPComplete · concepts/Lax117614/GraphCrawlingNPComplete.lean · lax-117614

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

    The graph crawling problem is NP-complete, in the sense of the NP core: it is definable in existential second-order logic, and every problem of NP reduces to it by an ordered first-order reduction. This is Proposition 4 of Gauquier, Manolescu and Senellart (EDBT 2026) at unit page costs, hardness coming from Set Cover by the paper's reduction.

    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

    Lean source view on GitHub

    1import Lax904597.Classes
    2import Lax799700.Problems
    3import Lax117614.WebsiteGraphs
    4import Lax117614.GraphCrawlingProblem
    5
    6/-!
    7---
    8title: Graph crawling is NP-complete
    9type: theorem
    10---
    11The graph crawling problem is NP-complete, in the sense of the NP core: it
    12is definable in existential second-order logic, and every problem of NP
    13reduces to it by an ordered first-order reduction. This is Proposition 4 of
    14Gauquier, Manolescu and Senellart (EDBT 2026) at unit page costs, hardness
    15coming from Set Cover by the paper's reduction.
    16-/
    17
    18namespace Lax117614.GraphCrawlingNPComplete
    19
    20open Lax904597.Classes Lax117614.GraphCrawlingProblem
    21
    22/-- GraphCrawling is NP-complete (Proposition 4 of the paper). -/
    23axiom graphCrawling_NP_complete : NP.Complete GraphCrawling
    24
    25end Lax117614.GraphCrawlingNPComplete
    26
    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…