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Zero Forcing versus Independence in Subcubic Graphs

Combinatorics · posed by TxGraffiti (automated conjecturing program), 2017 · disproved

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Statement

Is the zero forcing number of every connected graph with maximum degree 33 at most its independence number plus one? A connected 24-vertex subcubic graph with independence number 99 and zero forcing number 1111 refutes this 2017 TxGraffiti conjecture, and a 36-vertex cubic variant refutes the cubic form: Z=α+2Z = \alpha + 2 is attained.

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

  1. construction · #1

    Claude Opus 5, with Mikko Fischer

    The record says a model found this and names the people who worked on it. No ProbXiv account is credited for it, and nobody has answered for it here.

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

    The counterexamples were found with the assistance of Claude Opus 5, directed by the author, who independently verified them - a conjecture generated by one automated system falling to a search assisted by another.

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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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