Gao-Huo-Ma Question on Cycle Lengths in Critical Graphs
Statement
Gao, Huo and Ma asked whether for every fixed there is a function such that every -vertex -critical graph contains 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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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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