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@article{Liu2018CycleLA, title={Cycle lengths and minimum degree of graphs}, author={Chun-Hung Liu and Jie Ma}, journal={J. Comb. Theory, Ser. B}, year={2018}, volume={128}, pages={66-95} }

- Published in J. Comb. Theory, Ser. B 2018
DOI:10.1016/j.jctb.2017.08.002

There has been extensive research on cycle lengths in graphs with large minimum degree. In this paper, we obtain several new and tight results in this area. Let G be a graph with minimum degree at least k + 1. We prove that if G is bipartite, then there are k cycles in G whose lengths form an arithmetic progression with common difference two. For general graph G, we show that G contains ⌊k/2⌋ cycles with consecutive even lengths and k − 3 cycles whose lengths form an arithmetic progression with… CONTINUE READING