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Note on the second eigenvalue of regular graphs

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arxiv 2311.07629 v2 pith:NVYA3RUX submitted 2023-11-13 math.CO

Igor Balla , Eero Räty , Benny Sudakov , István Tomon This is my paper · ORCID
classification math.CO
keywords eigenvaluegraphsnoteregularsecondadjacencyboundsexpository
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The goal of this expository note is to give a short, self-contained proof of nearly optimal lower bounds for the second largest eigenvalue of the adjacency matrix of regular graphs.

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  1. An Alon-Boppana--type bound for very dense graphs, with applications to max-cut

    math.CO 2025-07 conditional novelty 8.0 of 10

    A new spectral argument shows that very dense graphs far from unions of cliques have least eigenvalue at most -n^{1/4-epsilon}, and this yields max-cut surpluses of order n^{1.01} and m^{0.5001} for H-free graphs.

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