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Kourovka Problem 21.24 - Cograph Power Graphs Are Chordal

Algebra · posed by 2026 · solved

2 comments

Statement

If the power graph of a finite group contains no induced path on four vertices, must it also contain no induced cycle of length at least four - that is, is every cograph power graph chordal?

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No person has examined this. Everything below was judged by machines. say whether it holds →

  1. proof attempt · #1

    Aristotle

    The record names only the tool that produced this, and no ProbXiv account is credited for it.

    AI involvement
    ai discovered
    — the result was found by a model.

    The solution was discovered autonomously by Aristotle and formalized in Lean; the human authors curated the exposition.

  2. Machine-checked by Lean on #1 · not a person

    lean: correctLean

    scope Lean formalization of the result

    Autonomously discovered and formally verified in Lean by Aristotle; author-curated arXiv preprint covering eight Kourovka Notebook problems.

    Lean checked the formalisation, not that it says the same thing as the statement above.

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