Author

M. Zhukovskii

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Preprint Aug 2026

Universality in random graphs via optimal linking systems: trees and beyond

We develop a framework for proving universality results in sparse random graphs. As a first application, we show that there exists an absolute constant $C>1$ such that, with high probability, for every fixed constant $\Delta$, the binomial random graph $G(n,C\ln n/n)$ contains every $n$-vertex tree with maximum degree...

Asaf Cohen Antonir, Lyuben Lichev, M. Zhukovskii · 1 citation

Preprint Aug 2026

A Local Central Limit Theorem for Clique Counts in Sparse Random Graphs

Let $X_H$ denote the number of copies of a fixed graph $H$ in $G_{n, p}$. Gilmer and Kopparty conjectured that $X_H$ satisfies a local central limit theorem (LCLT) provided that $H$ is connected, $p \gg n^{-1/m(H)}$, and $n^2 (1-p) \gg 1$, where $m(H)$ is the maximum density. Following the work of Berkowitz, Sah and Sa...

Asaf Cohen Antonir, Ilay Hoshen, M. Zhukovskii · 1 citation