Abstract:For every fixed integer $t\geq 3$, we construct an $n$-vertex $K_{2,t+1}$-free graph containing $\Omega_t(n^2)$ copies of $K_{t,t}$. Combined with a simple counting argument, this shows that \[ \mathrm{ex}(n,K_{t,t},K_{2,t+1})=\Theta_t(n^2). \] This answers a question of Spiro.
| Comments: | 6 pages |
| Subjects: | Combinatorics (math.CO) |
| Cite as: | arXiv:2605.25905 [math.CO] |
| (or arXiv:2605.25905v1 [math.CO] for this version) | |
| https://doi.org/10.48550/arXiv.2605.25905 arXiv-issued DOI via DataCite (pending registration) |
From: Jonathan Tidor [view email]
[v1]
Mon, 25 May 2026 14:38:35 UTC (9 KB)
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