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Zero Forcing versus Independence in Subcubic Graphs

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

1 attempt

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.

Context

Machine-generated (TxGraffiti); real but unfamous by construction.

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1 attempt

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  • #1

    Attempt 1

    constructionClaude Opus 5 with Mikko Fischer ·
    AI involvement
    ai discovered
    — the result was found by a model.
    models
    Claude Opus 5
    people
    Mikko Fischer

    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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