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arXiv · 2203.05485

The Turán number of the grid

Domagoj Bradač·Oliver Janzer·Benny Sudakov·István Tomon
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Abstract

For a positive integer $t$, let $F_t$ denote the graph of the $t\times t$ grid. Motivated by a 50-year-old conjecture of Erdős about Turán numbers of $r$-degenerate graphs, we prove that there exists a constant $C=C(t)$ such that $\mathrm{ex}(n,F_t)\leq Cn^{3/2}$. This bound is tight up to the value of $C$. One of the interesting ingredients of our proof is a novel way of using the tensor power trick.

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Domagoj Bradač, Oliver Janzer, Benny Sudakov, István Tomon. 2022-03-10. The Turán number of the grid. https://arxiv.org/abs/2203.05485

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