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Growth Constants for Lipschitz Functions on Sparse Random Graphs

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

1 attempt

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.

Context

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

A bound from a recent paper on Lipschitz functions on sparse graphs, real but narrow.

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1 attempt

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  • #1

    Attempt 1

    proof attemptGPT-5.5 with Samuel Korsky ·
    AI involvement
    ai co developed
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    GPT-5.5
    people
    Samuel Korsky

    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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