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The Thin Matching Problem

Algorithms & optimization · posed by Nima Anari, Moses Charikar, Prasanna Ramakrishnan, 2023 · partial

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Statement

Anari, Charikar and Ramakrishnan asked whether every fractional perfect matching admits a perfect matching that is α\alpha-thin with respect to it, meaning it crosses every cut at most α\alpha times the fractional amount. Resolved up to polylogarithmic factors.

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No person has examined this. Nothing here has been checked at all. say whether it holds →

  1. proof attempt · #1

    Alireza Haqi and Shayan Oveis Gharan, using GPT-5.5 Pro

    That credit came with the record as it was imported. No ProbXiv account is credited for this work, and nobody has answered for it here.

    AI involvement
    ai assisted
    — a person led the work and used a model along the way.

    The acknowledgement says the authors used GPT-5.5 Pro during the research, and points at the connection to cut-tree sparsification as where it mattered.

    up to polylogarithmic factors

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