Cycle lengths and minimum degree of graphs

@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}
}
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

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