Claw-free bricks that every $b$-invariant edge is solitary
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_ | 1866914060767854592 |
|---|---|
| author | Zhang, Yipei Wang, Xiumei |
| author_facet | Zhang, Yipei Wang, Xiumei |
| contents | A graph $G$ is a brick if it is 3-connected and $G-\{u,v\}$ has a perfect matching for any two distinct vertices $u$ and $v$ of $G$. Lucchesi and Murty proposed a problem concerning the characterization of bricks, distinct from $K_4$, $\overline{C_6}$ and the Petersen graph, in which every $b$-invariant edge is solitary. In this paper, we present a characterization of this problem when the bricks are claw-free. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_23114 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Claw-free bricks that every $b$-invariant edge is solitary Zhang, Yipei Wang, Xiumei Combinatorics A graph $G$ is a brick if it is 3-connected and $G-\{u,v\}$ has a perfect matching for any two distinct vertices $u$ and $v$ of $G$. Lucchesi and Murty proposed a problem concerning the characterization of bricks, distinct from $K_4$, $\overline{C_6}$ and the Petersen graph, in which every $b$-invariant edge is solitary. In this paper, we present a characterization of this problem when the bricks are claw-free. |
| title | Claw-free bricks that every $b$-invariant edge is solitary |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2509.23114 |