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

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

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Statement

Gao, Huo and Ma asked whether for every fixed k≥3k \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.

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  1. construction · #1

    Xiaozheng Chen and Bo Ning, using ChatGPT 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.

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

    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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