Explicit near-Ramanujan graphs of every degree

Ryan O'Donnell
For every constant d >= 3 and epsilon > 0, we give a deterministic poly(n)-time algorithm that outputs a d-regular graph on Î (n) vertices that is epsilon-near-Ramanujan; i.e., its eigenvalues are bounded in magnitude by 2sqrt(d-1)+epsilon (excluding the single trivial eigenvalue of d).
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