Matrix Quasi-tree Theorem
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_ | 1866912738287026176 |
|---|---|
| author | Deng, Qingying Jin, Xian'an Yan, Qi Yan, Yexiang |
| author_facet | Deng, Qingying Jin, Xian'an Yan, Qi Yan, Yexiang |
| contents | Building on prior work that established Matrix Quasi-tree Theorems for special embedded graphs, in this paper, we develop a comprehensive theory applicable to all embedded graphs. We introduce symbolic skew-adjacency matrices and reduction maps as key innovations, and prove that a specific polynomial derived from these matrices encodes all spanning quasi-trees of a bouquet. This result provides a complete analogue of the Matrix Tree Theorem for topological graph theory, with applications to quasi-tree enumeration in both orientable and non-orientable embedded graphs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_00680 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Matrix Quasi-tree Theorem Deng, Qingying Jin, Xian'an Yan, Qi Yan, Yexiang Combinatorics Building on prior work that established Matrix Quasi-tree Theorems for special embedded graphs, in this paper, we develop a comprehensive theory applicable to all embedded graphs. We introduce symbolic skew-adjacency matrices and reduction maps as key innovations, and prove that a specific polynomial derived from these matrices encodes all spanning quasi-trees of a bouquet. This result provides a complete analogue of the Matrix Tree Theorem for topological graph theory, with applications to quasi-tree enumeration in both orientable and non-orientable embedded graphs. |
| title | Matrix Quasi-tree Theorem |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2512.00680 |