Roman Vershynin

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math.CO2024

Hamiltonicity of Sparse Pseudorandom Graphs

Asaf Ferber, Jie Han, Dingjia Mao +1

We show that every $(n, d, λ)$ -graph contains a Hamilton cycle for sufficiently large $n$ , assuming that $d \geq lo g^{6} n$ and $λ \leq c d$ , where $c = \frac{1}{70000}$ . This significant…

math.CO2023

Covering the hypercube, the uncertainty principle, and an interpolation formula

Paata Ivanisvili, Ohad Klein, Roman Vershynin

We show that the minimal number of skewed hyperplanes that cover the hypercube ${0, 1}^{n}$ is at least $\frac{n}{2} + 1$ , and there are infinitely many $n$ 's when the hypercube can…