Generalized planar Turán numbers related to short cycles
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , |
|---|---|
| Format: | Preprint |
| Publié: |
2024
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866916245407793152 |
|---|---|
| author | Győri, Ervin Karim, Hilal Hama |
| author_facet | Győri, Ervin Karim, Hilal Hama |
| contents | Given two graphs $H$ and $F$, the generalized planar Turán number $\mathrm{ex}_\mathcal{P}(n,H,F)$ is the maximum number of copies of $H$ that an $n$-vertex $F$-free planar graph can have. We investigate this function when $H$ and $F$ are short cycles. Namely, for large $n$, we find the exact value of $\mathrm{ex}_\mathcal{P}(n, C_l,C_3)$, where $C_l$ is a cycle of length $l$, for $4\leq l\leq 6$, and determine the extremal graphs in each case. Also, considering the converse of these problems, we determine sharp upper bounds for $\mathrm{ex}_\mathcal{P}(n,C_3,C_l)$, for $4\leq l\leq 6$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_08162 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Generalized planar Turán numbers related to short cycles Győri, Ervin Karim, Hilal Hama Combinatorics Given two graphs $H$ and $F$, the generalized planar Turán number $\mathrm{ex}_\mathcal{P}(n,H,F)$ is the maximum number of copies of $H$ that an $n$-vertex $F$-free planar graph can have. We investigate this function when $H$ and $F$ are short cycles. Namely, for large $n$, we find the exact value of $\mathrm{ex}_\mathcal{P}(n, C_l,C_3)$, where $C_l$ is a cycle of length $l$, for $4\leq l\leq 6$, and determine the extremal graphs in each case. Also, considering the converse of these problems, we determine sharp upper bounds for $\mathrm{ex}_\mathcal{P}(n,C_3,C_l)$, for $4\leq l\leq 6$. |
| title | Generalized planar Turán numbers related to short cycles |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2405.08162 |