The planar Turan number of double star S_(3,5)
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , |
|---|---|
| Format: | Preprint |
| Publié: |
2025
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866916814192115712 |
|---|---|
| author | Liu, Dandan Xu, Shoujun |
| author_facet | Liu, Dandan Xu, Shoujun |
| contents | Given a graph H and a positive integer n, the planar Turan number of H, denoted by exp(n, H), is the maximum number of edges in an n-vertex H-free planar graph.D.Ghosh, et al.initiated the topic of double stars S_(k,l). Recently Xu et al.[AIMS Mathematics, 2025, 10(1): 1628-1644.] mentioned that exp(n, S_(3,5)) is still unknown.In this paper, we first establish that the planar Turan number S_(3,5) satisfies exp(n, S_(3,5)) <= 23n/8 - 9/2 for all n >= 2. The upper bound is tight for n = 12. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_03487 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The planar Turan number of double star S_(3,5) Liu, Dandan Xu, Shoujun Combinatorics Given a graph H and a positive integer n, the planar Turan number of H, denoted by exp(n, H), is the maximum number of edges in an n-vertex H-free planar graph.D.Ghosh, et al.initiated the topic of double stars S_(k,l). Recently Xu et al.[AIMS Mathematics, 2025, 10(1): 1628-1644.] mentioned that exp(n, S_(3,5)) is still unknown.In this paper, we first establish that the planar Turan number S_(3,5) satisfies exp(n, S_(3,5)) <= 23n/8 - 9/2 for all n >= 2. The upper bound is tight for n = 12. |
| title | The planar Turan number of double star S_(3,5) |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2503.03487 |