Author

D. Mubayi

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Preprint Sep 2026

Sharper Zarankiewicz and Diagonal Bipartite Ramsey Bounds

We prove that there is an absolute positive constant $c$ such that every bipartite graph with $N$ vertices in each part and at least $N^2/2$ edges contains a complete bipartite graph $K_{t,t}$ whenever $N\ge c\, 2^{t}$. This improves the classical K\H{o}v\'ari-S\'os-Tur\'an bound requiring $N$ of order $t\,2^t $. As a...

D. Mubayi · 0 citations

Preprint Sep 2026

Maximizing $K_r + I_r$ in graphs with fixed edge density

For every integer $r\ge4$, and $\rho \in [0,1]$, we asymptotically determine the maximum proportion of $r$-element sets of vertices that induce either a clique or an independent set in a large graph with density $\rho$. This generalizes a result of Olpp for $r=3$. After the initial idea for the main proof was found by...

J'ozsef Balogh, Andrzej Grzesik, Bernard Lidický et al. · 0 citations