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Sharp Hardness for MAX-3-CUT

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max-3-cut-sharp-hardnessTheoretical computer scienceposed by S. Khot, G. Kindler, E. Mossel, R. O'Donnell, 2004recorded: solved

1 attempt · no person has looked

Statement

Assuming the Unique Games Conjecture, it is NP-hard to approximate MAX-3-CUT better than the Frieze-Jerrum semidefinite program does, and similarly for Quantum MAX-CUT: the sharpness question in the Khot-Kindler-Mossel-O'Donnell line, connected to the Plurality is Stablest problem.

Context

Sharp inapproximability for MAX-k-CUT has stood open since Khot-Kindler-Mossel-O'Donnell (2004) and is known across the approximation-algorithms community.

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  • #1

    Attempt 1

    proof attemptChatGPT 5.6 with Steven Heilman ·
    AI involvement
    ai assisted
    — a person led the work and used a model along the way.
    models
    ChatGPT 5.6
    people
    Steven Heilman

    ChatGPT 5.6 assisted in the preparation of the manuscript, including producing the spectral certificates in Propositions 4.1 and 4.4 and Lemmas 9.3 and A.4 - proof components, not prose.

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