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Sabidussi's Compatibility Conjecture

Combinatorics · posed by Gert Sabidussi · solved

2 comments

Statement

Can the edges of a finite connected multigraph, given a closed eulerian trail, be partitioned into circuits so that no circuit contains two edges used consecutively in the trail? The proof in fact four-colours the edges to satisfy the constraints.

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

  1. proof attempt · #1

    Nikolay Ulyanov, using GPT-5.6 Pro, GPT-5.6 Sol

    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.

    Developed with GPT-5.6 Pro and GPT-5.6 Sol; the author reviewed the proof.

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

    lean: correctLean

    scope Lean formalization of the result

    Lean 4 formalization available in the author's repository, alongside the arXiv preprint.

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

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Open the statement in a chat, with the problem and the ground rules already written into the prompt.

open in Claude →open in ChatGPT →

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