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Boots-Royle/Cao-Vince Conjecture on Planar Spectral Radius

Combinatorics · posed by Barry Boots, Gordon Royle; Dasong Cao, Andrew Vince, 1991 · solved

1 attempt

Statement

Boots and Royle, and independently Cao and Vince, conjectured that the join of an edge with a path on n2n-2 vertices is the unique planar graph of maximum adjacency spectral radius for every n9n \ge 9. Tait and Tobin proved it for sufficiently large nn in 2017; the conjecture now holds for all n9n \ge 9.

Context

A conjecture posed independently by two groups around 1991 and a standard reference point in spectral extremal graph theory, with Tait and Tobin's asymptotic solution in JCTB.

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Attempts

1 attempt

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  • #1

    Attempt 1

    proof attemptChatGPT with Lele Liu, Bo Ning, Yi Wang ·
    AI involvement
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    a person led the work and used a model along the way.
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    ChatGPT
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    Lele Liu, Bo Ning, Yi Wang

    The declaration credits the model with generating the code that searched for extremal planar graphs, and with assisting in several computations and symbolic derivations, alongside language polishing.

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