Explicit near-Ramanujan graphs of every degree

@article{Mohanty2020ExplicitNG,
  title={Explicit near-Ramanujan graphs of every degree},
  author={Sidhanth Mohanty and R. O'Donnell and Pedro Paredes},
  journal={Proceedings of the 52nd Annual ACM SIGACT Symposium on Theory of Computing},
  year={2020}
}
For every constant d ≥ 3 and є > 0, we give a deterministic poly(n)-time algorithm that outputs a d-regular graph on Θ(n) vertices that is є-near-Ramanujan; i.e., its eigenvalues are bounded in magnitude by 2√d−1 + є (excluding the single trivial eigenvalue of d). 

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Lifts, Discrepancy and Nearly Optimal Spectral Gaps