Discoveries / combinatorics

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.