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The Frankl-Peng-Rodl-Talbot Question on Turan Density Intervals

Combinatorics · posed by Peter Frankl, Yuejian Peng, Vojtech Rodl, John Talbot, 2007 · solved

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Statement

Frankl, Peng, Rodl and Talbot asked in 2007 whether the set of Turan densities of families of rr-graphs contains intervals. It does: for every r≥3r \ge 3 the set contains non-degenerate intervals, including one of the form [1−δr,1][1-\delta_r, 1].

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

  1. construction · #1

    Xizhi Liu and Oleg Pikhurko, using ChatGPT 5.4 Pro, ChatGPT 5.4 Thinking

    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.

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

    The credit is bounded and precise: the graphs for the internal spectral gadget were suggested by the models, and the authors state the other main ideas and constructions are theirs.

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