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A proof of Alon’s second eigenvalue conjecture and related problems
About this Title
Joel Friedman
Publication: Memoirs of the American Mathematical Society
Publication Year:
2008; Volume 195, Number 910
ISBNs: 978-0-8218-4280-5 (print); 978-1-4704-0516-8 (online)
DOI: https://doi.org/10.1090/memo/0910
MathSciNet review: 2437174
MSC: Primary 05C50; Secondary 05C80, 05C81, 68R10
Table of Contents
Chapters
- 1. Introduction
- 2. Problems with the standard trace method
- 3. Background and terminology
- 4. Tangles
- 5. Walk sums and new types
- 6. The selective trace
- 7. Ramanujan functions
- 8. An expansion for some selective traces
- 9. Selective traces in graphs with (without) tangles
- 10. Strongly irreducible traces
- 11. A sidestepping lemma
- 12. Magnification theorems
- 13. Finishing the $\mathcal {G}_{n,d}$ proof
- 14. Finishing the proofs of the main theorems
- 15. Closing remarks