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Gao-Huo-Ma Question on Cycle Lengths in Critical Graphs

Combinatorics · posed by Gao, Huo, Ma, 2021 · solved

1 attempt

Statement

Gao, Huo and Ma asked whether for every fixed k3k \ge 3 there is a function fk(n)f_k(n) \to \infty such that every nn-vertex (k+1)(k+1)-critical graph contains fk(n)f_k(n) consecutive cycle lengths. The paper settles this and two related problems on cycle lengths and cycles with chords under chromatic and degree constraints.

Context

A numbered question from a 2021 paper on cycle lengths in critical graphs, with a documented but specialized following.

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Attempts

1 attempt

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  • #1

    Attempt 1

    constructionChatGPT 5.5 with Xiaozheng Chen, Bo Ning ·
    AI involvement
    ai assisted
    a person led the work and used a model along the way.
    models
    ChatGPT 5.5
    people
    Xiaozheng Chen, Bo Ning

    The declaration says the model was used in the search for the construction in Theorem 1.2, starting from a requirement based on the Hajos join that the second author supplied, and that the present construction emerged after several rounds of refinement, discussion and checking. It also helped with proofreading.

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