Criteria on forbidden subgraphs in the complements for positive Lin--Lu--Yau curvature
Fuente:
arXiv
Guardado en:
| Autores principales: | , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2026
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866909013688451072 |
|---|---|
| author | Chen, Kaizhe Liu, Shiping You, Zhe |
| author_facet | Chen, Kaizhe Liu, Shiping You, Zhe |
| contents | We investigate forbidden subgraph conditions in the complement of a graph that guarantee positive Lin--Lu--Yau curvature. In particular, we prove that every graph whose complement contains no $4$-cycles has positive Lin--Lu--Yau curvature, with the only exception of the $4$-vertex path. We further prove that, for any integer $t\ge2$, every graph on at least $\max\{t^2-2t+2, 8t\}$ vertices whose complement contains no $K_{2,t}$ has positive curvature. In addition, this lower bound on the number of vertices is optimal for $t\geq 10$. Finally, we construct examples showing that, in general, the forbidden subgraphs in these results cannot be replaced by cycles of length other than $4$ or by complete bipartite graphs $K_{s,t}$ with $s> 2$ and $t> 2$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_03470 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Criteria on forbidden subgraphs in the complements for positive Lin--Lu--Yau curvature Chen, Kaizhe Liu, Shiping You, Zhe Combinatorics Differential Geometry We investigate forbidden subgraph conditions in the complement of a graph that guarantee positive Lin--Lu--Yau curvature. In particular, we prove that every graph whose complement contains no $4$-cycles has positive Lin--Lu--Yau curvature, with the only exception of the $4$-vertex path. We further prove that, for any integer $t\ge2$, every graph on at least $\max\{t^2-2t+2, 8t\}$ vertices whose complement contains no $K_{2,t}$ has positive curvature. In addition, this lower bound on the number of vertices is optimal for $t\geq 10$. Finally, we construct examples showing that, in general, the forbidden subgraphs in these results cannot be replaced by cycles of length other than $4$ or by complete bipartite graphs $K_{s,t}$ with $s> 2$ and $t> 2$. |
| title | Criteria on forbidden subgraphs in the complements for positive Lin--Lu--Yau curvature |
| topic | Combinatorics Differential Geometry |
| url | https://arxiv.org/abs/2605.03470 |