Disjoint chorded cycles in a $2$-connected graph
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , |
|---|---|
| Format: | Preprint |
| Publié: |
2025
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866913854332600320 |
|---|---|
| author | Lu, Zaiping Xue, Shudan |
| author_facet | Lu, Zaiping Xue, Shudan |
| contents | A chorded cycle in a graph $G$ is a cycle on which two nonadjacent vertices are adjacent in the graph $G$. In 2010, Gao and Qiao independently proved a graph of order at least $4s$, in which the neighborhood union of any two nonadjacent vertices has at least $4s+1$ vertices, contains $s$ vertex-disjoint chorded cycles. In 2022, Gould raised a problem that asks whether increasing connectivity would improve the neighborhood union condition. In this paper, we solve the problem for $2$-connected graphs by
proving that a $2$-connected graph of order at least $4s$, in which the neighborhood union of any two nonadjacent vertices has at least $4s$ vertices, contains $s$ vertex-disjoint chorded cycles. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_09477 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Disjoint chorded cycles in a $2$-connected graph Lu, Zaiping Xue, Shudan Combinatorics A chorded cycle in a graph $G$ is a cycle on which two nonadjacent vertices are adjacent in the graph $G$. In 2010, Gao and Qiao independently proved a graph of order at least $4s$, in which the neighborhood union of any two nonadjacent vertices has at least $4s+1$ vertices, contains $s$ vertex-disjoint chorded cycles. In 2022, Gould raised a problem that asks whether increasing connectivity would improve the neighborhood union condition. In this paper, we solve the problem for $2$-connected graphs by proving that a $2$-connected graph of order at least $4s$, in which the neighborhood union of any two nonadjacent vertices has at least $4s$ vertices, contains $s$ vertex-disjoint chorded cycles. |
| title | Disjoint chorded cycles in a $2$-connected graph |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2504.09477 |