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

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tournament-isomorphism-bounded-vc-dimensionTheoretical computer scienceposed by Daniel Neuen, Martin Groherecorded: solved

1 attempt · no person has looked

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.

Context

A posed open problem in the graph-isomorphism literature after Babai's quasipolynomial breakthrough, from named experts, with a clean parameterized resolution. Specialist - just above the numbered-problem band.

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  • #1

    Attempt 1

    proof attemptClaude Sonnet 5 with Simon Rassmann, Pascal Schweitzer ·
    AI involvement
    ai co developed
    — a person and a model developed the result together.
    models
    Claude Sonnet 5
    people
    Simon Rassmann, Pascal Schweitzer

    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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