Cycles of consecutive lengths in $3$-connected graphs
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866915454045388800 |
|---|---|
| author | Li, Chengli Zhan, Xingzhi |
| author_facet | Li, Chengli Zhan, Xingzhi |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_14915 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Cycles of consecutive lengths in $3$-connected graphs Li, Chengli Zhan, Xingzhi Combinatorics 05C38, 05C07, 05C40 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. |
| title | Cycles of consecutive lengths in $3$-connected graphs |
| topic | Combinatorics 05C38, 05C07, 05C40 |
| url | https://arxiv.org/abs/2508.14915 |