18.217 Graph Theory and Additive Combinatorics
18.217 Graph Theory and Additive Combinatorics (Fall 2019, MIT OCW). Instructor: Professor Yufei Zhao. This course examines classical and modern developments in graph theory and additive combinatorics, with a focus on topics and themes that connect the two subjects. The course also introduces students to current research topics and open problems. (from ocw.mit.edu)
| Lecture 08 - Szemeredi's Graph Regularity Lemma III: Further Applications |
After proving Roth's theorem last lecture, Professor Zhao explains Behrend's construction of large sets of integers without 3-term arithmetic progressions, as well as another application of the triangle removal lemma to subsets of a 2-dimensional lattice without corners.
The second half of the lecture discusses further applications of the regularity method within graph theory: graph embedding, counting, and removal lemmas, as well as a proof of the Erdos-Stone-Simonovits theorem on H-free graphs.
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