$K_{2,t+1}$-free graphs with many copies of $K_{t,t}$
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866914599685586944 |
|---|---|
| author | Pohoata, Cosmin Tidor, Jonathan Yu, Hung-Hsun Hans |
| author_facet | Pohoata, Cosmin Tidor, Jonathan Yu, Hung-Hsun Hans |
| contents | For every fixed integer $t\geq 3$, we construct an $n$-vertex $K_{2,t+1}$-free graph containing $Ω_t(n^2)$ copies of $K_{t,t}$. Combined with a simple counting argument, this shows that \[ \mathrm{ex}(n,K_{t,t},K_{2,t+1})=Θ_t(n^2). \] This answers a question of Spiro. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_25905 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | $K_{2,t+1}$-free graphs with many copies of $K_{t,t}$ Pohoata, Cosmin Tidor, Jonathan Yu, Hung-Hsun Hans Combinatorics For every fixed integer $t\geq 3$, we construct an $n$-vertex $K_{2,t+1}$-free graph containing $Ω_t(n^2)$ copies of $K_{t,t}$. Combined with a simple counting argument, this shows that \[ \mathrm{ex}(n,K_{t,t},K_{2,t+1})=Θ_t(n^2). \] This answers a question of Spiro. |
| title | $K_{2,t+1}$-free graphs with many copies of $K_{t,t}$ |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2605.25905 |