{
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  "problem_id": "vibemathed:gao-huo-ma-consecutive-cycle-lengths",
  "title": "Gao-Huo-Ma Question on Cycle Lengths in Critical Graphs",
  "canonical_statement": "Gao, Huo and Ma asked whether for every fixed $k \\ge 3$ there is a function $f_k(n) \\to \\infty$ such that every $n$-vertex $(k+1)$-critical graph contains $f_k(n)$ consecutive cycle lengths. The paper settles this and two related problems on cycle lengths and cycles with chords under chromatic and degree constraints.",
  "plain_summary": "VibeMathed reports this item as resolved. VibeMath preserves that report as a source assertion and has not independently authored a plain-language mathematical explanation.",
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      "type": "proved",
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      "occurred_at": "2026-07-16T00:00:00.000Z",
      "title": "arXiv:2607.15501 - Cycle lengths and chords under chromatic and degree constraints",
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      "attempted_at": "2026-07-16T00:00:00.000Z",
      "human_collaborators": [
        "Xiaozheng Chen",
        "Bo Ning"
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      "prompt_public": null,
      "outcome": "The declaration says the model was used in the search for the construction in Theorem 1.2, starting from a requirement based on the Hajos join that the second author supplied, and that the present construction emerged after several rounds of refinement, discussion and checking. It also helped with proofreading.",
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    {
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  "generated_at": "2026-09-13T16:28:40.178Z"
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