Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2511.22361 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866912734197579776 |
|---|---|
| author | Lian, Liwen Liu, Jinfeng Niu, Mengyuan Wang, Xiumei |
| author_facet | Lian, Liwen Liu, Jinfeng Niu, Mengyuan Wang, Xiumei |
| contents | A connected nontrivial graph $G$ is {\it matching covered} if every edge of $G$ is contained in some perfect matching of $G$. A matching covered graph $G$ is {\it minimal} if $G-e$ is not matching covered for each edge $e$ of $G$. A graph is said to be {\it factor-critical} if $G-v$ has a perfect matching for every $v\in V(G)$. A factor-critical graph $G$ is said to be {\it minimal factor-critical} if $G-e$ is not factor-critical graph for each edge $e\in E(G)$. In this paper, by employing ear decomposition and edge-exchange techniques, the greatest spectral radii of minimal matching covered bipartite graphs and minimal factor-critical graphs are determined, and the corresponding extremal graphs are characterized. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_22361 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The spectral radii and extremal graphs of two types of minimal graphs Lian, Liwen Liu, Jinfeng Niu, Mengyuan Wang, Xiumei Combinatorics A connected nontrivial graph $G$ is {\it matching covered} if every edge of $G$ is contained in some perfect matching of $G$. A matching covered graph $G$ is {\it minimal} if $G-e$ is not matching covered for each edge $e$ of $G$. A graph is said to be {\it factor-critical} if $G-v$ has a perfect matching for every $v\in V(G)$. A factor-critical graph $G$ is said to be {\it minimal factor-critical} if $G-e$ is not factor-critical graph for each edge $e\in E(G)$. In this paper, by employing ear decomposition and edge-exchange techniques, the greatest spectral radii of minimal matching covered bipartite graphs and minimal factor-critical graphs are determined, and the corresponding extremal graphs are characterized. |
| title | The spectral radii and extremal graphs of two types of minimal graphs |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2511.22361 |