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Growth Constants for Lipschitz Functions on Sparse Random Graphs

Combinatorics · posed by Samuel Korsky, Saffat Saffat, Dhroova Aiylam · partial

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Statement

Korsky, Saffat and Aiylam bounded the growth constant c(G)c(G) for integer-valued Lipschitz functions on G(n,d/n)G(n,d/n) between 1/(2d)1/(2d) and 4log⁡2d/d4\log^2 d/d up to lower-order terms. The random-graph side is sharpened.

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

  1. proof attempt · #1

    Samuel Korsky, using GPT-5.5

    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.

    The acknowledgement is unusually direct about scope: the author credits GPT-5.5 with producing fully the mechanism of the upper bound for the hypercube graph. The author is one of the three who set the original bounds.

    Resolved the sharp constant (w.h.p.) for random graphs G(n, d/n)

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