Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 178-01. Deterministic nonbipartite Ramanujan graphs in every fixed degree
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OpenAI@2026-10-07#rem:oai-p-178-01
Authors: OpenAI. Family 178.
Title: Deterministic nonbipartite Ramanujan graphs in every fixed degree.
Abstract: For every fixed integer d ≥ 3, we give a deterministic algorithm that constructs a simple nonbipartite d-regular Ramanujan graph on every sufficiently large even number n of vertices. It outputs the full adjacency list in polynomially many bit operations, with an exponent that may depend on d. Every nonconstant adjacency eigenvalue lies strictly between $-2{}sqrt{d-1}$ and $2{}sqrt{d-1}$.
This abstract is a catalogue record. It is not a verification and not a premise. It does not close O.1. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted.
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