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Neuen-Grohe Problem: Isomorphism of Tournaments with Bounded VC Dimension

Theoretical computer science · posed by Daniel Neuen, Martin Grohe · solved

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Statement

Among classes of tournaments for which neither hardness nor polynomial-time solvability of isomorphism was known, bounded VC dimension stood out as an open problem of Neuen and Grohe. Resolved: isomorphism of tournaments of VC dimension dd is decidable in time nO(dlog⁡d)n^{O(d \log d)}, so automorphism groups of bounded-VC tournaments are computable in polynomial time; isomorphism of tournaments of bounded chromatic number is also polynomial-time decidable.

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

  1. proof attempt · #1

    Simon Rassmann and Pascal Schweitzer, using Claude Sonnet 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 co developed
    — a person and a model developed the result together.

    The statement of AI use names two specific steps: the proof of one preliminary lemma (the tournament VC-dimension lemma) was provided by Claude Sonnet 5, and the proof of a second bound was simplified by it. Named model-contributed lemmas inside a human-led argument.

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