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Explicit Near-Ramanujan Graphs of Every Degree
SIAM Journal on Computing ( IF 1.2 ) Pub Date : 2021-02-23 , DOI: 10.1137/20m1342112
Sidhanth Mohanty , Ryan O'Donnell , Pedro Paredes

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


中文翻译:

每个度的显式近拉马努金图

SIAM 计算杂志,超前印刷。
对于每个常数 $d\geq 3$ 和 $\epsilon > 0$,我们给出一个确定性的 $\operatorname{poly}(n)$-time 算法,它在 $\Theta(n) 上输出 $d$-regular 图$\eps$-near-Ramanujan 的顶点;即,它的特征值的大小为 $2\sqrt{d-1} + \epsilon$(不包括 $d$ 的单个平凡特征值)。
更新日期:2021-02-23
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