A Unified Proof of Conjectures on Cycle Lengths in Graphs

  title={A Unified Proof of Conjectures on Cycle Lengths in Graphs},
  author={Jun-ming Gao and Qingyi Huo and Chun-Hung Liu and Jie Ma},
  journal={arXiv: Combinatorics},
In this paper, we prove a tight minimum degree condition in general graphs for the existence of paths between two given endpoints, whose lengths form a long arithmetic progression with common difference one or two. This allows us to obtain a number of exact and optimal results on cycle lengths in graphs of given minimum degree, connectivity or chromatic number. More precisely, we prove the following statements by a unified approach. (1) Every graph $G$ with minimum degree at least $k+1… 

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