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The Erdos-Lovasz Cover Number Problem

Combinatorics · posed by Paul Erdos, Laszlo Lovasz, 1975 · partial

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Statement

Let g(r)g(r) be the fewest edges in an rr-uniform intersecting hypergraph with cover number rr. Erdos and Lovasz proved g(r)≥8r/3−3g(r) \ge 8r/3 - 3. An elementary argument gives g(r)≥3r−4g(r) \ge 3r - 4, and building on it with Kahn's small-codegree edge-colouring theorem pushes the bound further.

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

  1. proof attempt · #1

    Varun Sivashankar, using ChatGPT 5.5 Pro, Aristotle

    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 co developed
    — a person and a model developed the result together.

    The acknowledgement states the proof was discovered with the help of ChatGPT 5.5 Pro, and that Theorem 1 was then formalized in Lean with Harmonic's Aristotle.

    an improved lower bound; the true order of g(r) remains open

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