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Erdos's Question on the Independence Ratio of Unit-Distance Graphs

Geometry & topology · posed by Paul Erdos · solved

1 comment

Statement

Erdos asked whether a finite unit-distance graph in the plane can have independence ratio below 1/41/4. One exists, built on the geometric fractional chromatic number framework of Matolcsi, Ruzsa, Varga and Zsamboki plus a carefully chosen two-vertex augmentation.

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

  1. computation · #1

    Akos Ducz and Daniel Varga, using ChatGPT, Codex (GPT-5.5)

    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 models were used for software development including code drafting and debugging, plus improvement and formatting suggestions. The search that produces the graph is computational, so the tooling is load-bearing even though no mathematical step is attributed.

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open in Claude →open in ChatGPT →

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