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

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

Result: Proved
Status: Resolved
AI contribution: AI-assisted
Method: Construction
Field: Graph theory
Posed by: Gao, Huo, Ma
Year posed: 2021
Years open: 5y
Solved: 2026-07-16
Model: ChatGPT 5.5
Vendor: OpenAI
Collaborators: Xiaozheng Chen, Bo Ning
Verification: Unreviewed
Publication: Preprint
Significance: 10 / 100
Disclosed cost: —
Wikipedia: No dedicated article

What the AI did

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.

Verification

arXiv preprint; not yet peer-reviewed.

Source

arXiv:2607.15501 - Cycle lengths and chords under chromatic and degree constraints

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

What the AI did

Verification

Source

Discussion