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A proof of alon's second eigenvalue conjecture
Abstract
A d-regular graph has largest or first (adjacency matrix) eigenvalue λ1 = d. In this paper we show the following conjecture of Alon. Fix an integer d > 2 and a real ε > 0. Then for sufficiently large n we have that "most" d-regular graphs on n vertices have all their eigenvalues except λ1 = d bounded above by 2√d-1 + ε. Our methods, being trace methods, also bound those eigenvalues below by -2√d-1 - ε.
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Metadata
- Authors
- Friedman, J.
- Venue
- Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
- Publisher
- ACM
- Published
- 2003-06-09
- Pages
- 720-724
- OpenAlex
- W1993418693
- Cited by
- 192
- References
- 0
- FWCI
- 25.98
- Type
- conference paper
- Language
- en
- Open access
- closed
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