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18.217 | Fall 2019 | Graduate

# Graph Theory and Additive Combinatorics

#### Lecture Videos

video
169 MB
Lecture 1: A bridge between graph theory and additive combinatorics
video
162 MB
Lecture 2: Forbidding a Subgraph I: Mantel’s Theorem and Turán’s Theorem
video
169 MB
Lecture 3: Forbidding a Subgraph II: Complete Bipartite Subgraph
video
176 MB
Lecture 4: Forbidding a Subgraph III: Algebraic Constructions
video
178 MB
Lecture 5: Forbidding a Subgraph IV: Dependent Random Choice
video
176 MB
Lecture 6: Szemerédi’s Graph Regularity Lemma I: Statement and Proof
video
166 MB
Lecture 7: Szemerédi’s Graph Regularity Lemma II: Triangle Removal Lemma
video
180 MB
Lecture 8: Szemerédi’s Graph Regularity Lemma III: Further Applications
video
184 MB
Lecture 9: Szemerédi’s Graph Regularity Lemma IV: Induced Removal Lemma
video
175 MB
Lecture 10: Szemerédi’s Graph Regularity Lemma V: Hypergraph Removal and Spectral Proof
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#### Assignments

pdf
482 kB
18.217 F2019 Problem Set

#### Lecture Notes

pdf
327 kB
18.217 F2019 Chapter 1: Introduction to graph theory and additive combinatorics
pdf
436 kB
18.217 F2019 Chapter 2: Forbidding subgraphs
pdf
479 kB
18.217 F2019 Chapter 3: Szemerédi’s regularity lemma
pdf
386 kB
18.217 F2019 Chapter 4: Pseudorandom graphs
pdf
419 kB
18.217 F2019 Chapter 5: Graph limits
pdf
379 kB
18.217 F2019 Chapter 6: Roth’s theorem
pdf
433 kB
18.217 F2019 Chapter 7: Structure of set addition
pdf
310 kB
18.217 F2019 Chapter 8: The sum-product problem
pdf
1 MB
18.217 F2019 Full Lecture Notes: Graph Theory and Additive Combinatorics

## Course Info

##### Instructor

- Prof. Yufei Zhao

##### Departments

- Mathematics

##### As Taught In

Fall 2019

##### Level

Graduate

##### Topics

- Mathematics
  - Applied Mathematics
  - Discrete Mathematics
  - Probability and Statistics

##### Learning Resource Types

theaters Lecture Videos
assignment Problem Sets
notes Lecture Notes
co_present Instructor Insights

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