Author

Lyuben Lichev

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Preprint Sep 2026

Long induced cycles in pseudorandom graphs

We show that, for some absolute constants $c_1,c_2>0$, every $(n,d,\lambda)$-graph with $\lambda\le c_1 d$ contains an induced cycle of length at least $c_2n\log(d/\lambda)/d$. This is best possible up to the values of $c_1,c_2$. Our techniques include a multi-scale algorithmic analysis, an adapted depth-first explorat...

Sahar Diskin, Lyuben Lichev, Michael Krivelevich et al. · 1 citation

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