Cycles of consecutive lengths in $3$-connected graphs

Chengli Li; Xingzhi Zhan

Cycles of consecutive lengths in $3$-connected graphs

Combinatorics 2025-08-22 v1

Authors: Chengli Li , Xingzhi Zhan

Abstract

Recently Lin, Wang and Zhou have proved that every $3$ -connected nonbipartite graph of minimum degree at least $k$ with $k\ge 6$ and order at least $k+2$ contains $k$ cycles of consecutive lengths. They also conjecture that this result is true for $k=4, 5.$ We prove this conjecture. Our proofs use many ideas of Gao, Huo, Liu and Ma.

Keywords

consecutive cycles 3-connected graph nonbipartite graph graph theory minimum degree

Cite

@article{arxiv.2508.14915,
  title  = {Cycles of consecutive lengths in $3$-connected graphs},
  author = {Chengli Li and Xingzhi Zhan},
  journal= {arXiv preprint arXiv:2508.14915},
  year   = {2025}
}

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17 pages

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