The minimum size of a $k$-connected locally nonforesty graph
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_ | 1866910797235486720 |
|---|---|
| author | Li, Chengli Tang, Yurui Zhan, Xingzhi |
| author_facet | Li, Chengli Tang, Yurui Zhan, Xingzhi |
| contents | A local subgraph of a graph is the subgraph induced by the neighborhood of a vertex. Thus a graph of order $n$ has $n$ local subgraphs. A graph $G$ is called locally nonforesty if every local subgraph of $G$ contains a cycle. Clearly, a graph is locally nonforesty if and only if every vertex of the graph is the hub of a wheel. We determine the minimum size of a $k$-connected locally nonforesty graph of order $n.$ |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_13980 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The minimum size of a $k$-connected locally nonforesty graph Li, Chengli Tang, Yurui Zhan, Xingzhi Combinatorics 05C35, 05C38, 05C40 A local subgraph of a graph is the subgraph induced by the neighborhood of a vertex. Thus a graph of order $n$ has $n$ local subgraphs. A graph $G$ is called locally nonforesty if every local subgraph of $G$ contains a cycle. Clearly, a graph is locally nonforesty if and only if every vertex of the graph is the hub of a wheel. We determine the minimum size of a $k$-connected locally nonforesty graph of order $n.$ |
| title | The minimum size of a $k$-connected locally nonforesty graph |
| topic | Combinatorics 05C35, 05C38, 05C40 |
| url | https://arxiv.org/abs/2501.13980 |