# A Unified Proof of Conjectures on Cycle Lengths in Graphs

@article{Gao2019AUP, 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}, year={2019} }

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…

## 12 Citations

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