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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

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Statement

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

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

  1. proof attempt · #1

    Lele Liu, Bo Ning and Yi Wang, using ChatGPT

    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 assisted
    — a person led the work and used a model along the way.

    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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