Interlacing Families IV: Bipartite Ramanujan Graphs of All Sizes

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Other Links: arxiv.org

Abstract:

We prove that there exist bipartite Ramanujan graphs of every degree and every number of vertices. The proof is based on analyzing the expected characteristic polynomial of a union of random perfect matchings, and involves three ingredients: (1) a formula for the expected characteristic polynomial of the sum of a regular graph with a ra...More

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