Book contents
- Frontmatter
- Contents
- Preface
- Part I Extremal Graph Theory
- Introduction to Part I
- 1 Matchings, Paths, and Cycles
- 2 Probabilistic Methods and Random Graphs
- 3 Turán’s Theorem
- 4 Extremal Problems for Bipartite Graphs
- 5 Moore Graphs and the Even Cycle Theorem
- 6 Random Constructions
- 7 Szemerédi’s Regularity Lemma
- 8 Pseudorandom Graphs
- 9 Graph Ramsey Theory
- 10 Constructions in Ramsey Theory
- Part II Extremal Set Theory and Hypergraph Theory
- Glossary of Notation
- References
- Index
8 - Pseudorandom Graphs
from Part I - Extremal Graph Theory
Published online by Cambridge University Press: aN Invalid Date NaN
Book contents
- Frontmatter
- Contents
- Preface
- Part I Extremal Graph Theory
- Introduction to Part I
- 1 Matchings, Paths, and Cycles
- 2 Probabilistic Methods and Random Graphs
- 3 Turán’s Theorem
- 4 Extremal Problems for Bipartite Graphs
- 5 Moore Graphs and the Even Cycle Theorem
- 6 Random Constructions
- 7 Szemerédi’s Regularity Lemma
- 8 Pseudorandom Graphs
- 9 Graph Ramsey Theory
- 10 Constructions in Ramsey Theory
- Part II Extremal Set Theory and Hypergraph Theory
- Glossary of Notation
- References
- Index
Summary
A natural starting point for the study of graphs with "random-like" properties is the notion of jumbled graphs, introduced by Thomason. We develop the properties of these pseudorandom graphs and study the related notion of quasirandom graphs and spectral properties of graphs, including (n, d, λ)-graphs, the expander mixing lemma, the Alon–Boppana Theorem, the Haemers–Hoffman–del Sarte bound, and the proof of the sensitivity conjecture.
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- Extremal Graph and Hypergraph TheoryWith Ramsey Theory, pp. 141 - 164Publisher: Cambridge University PressPrint publication year: 2026
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