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arXiv · 1909.06988

Explicit near-Ramanujan graphs of every degree

Sidhanth Mohanty·Ryan O'Donnell·Pedro Paredes
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Abstract

For every constant $d \geq 3$ and $ε> 0$, we give a deterministic $\mathrm{poly}(n)$-time algorithm that outputs a $d$-regular graph on $Θ(n)$ vertices that is $ε$-near-Ramanujan; i.e., its eigenvalues are bounded in magnitude by $2\sqrt{d-1} + ε$ (excluding the single trivial eigenvalue of~$d$).

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Sidhanth Mohanty, Ryan O'Donnell, Pedro Paredes. 2022-11-27. Explicit near-Ramanujan graphs of every degree. https://arxiv.org/abs/1909.06988

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