18.217 Graph Theory and Additive Combinatorics (Fall 2019, MIT OCW): Lecture 03 - Forbidding a Subgraph II: Complete Bipartite Subgraph

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 03 - Forbidding a Subgraph II: Complete Bipartite Subgraph

What is the maximum number of edges in a graph forbidding a cycle of length four? What about forbidding a complete bipartite graph of a fixed size? Professor Zhao discusses the Kovari-Sos-Turan theorem, which gives an upper bound. In the case of 4-cycles, a matching algebraic construction of a C4-free graph is also demonstrated.

Go to the Course Home or watch other lectures:

Lecture 01 - A Bridge between Graph Theory and Additive Combinatorics

Lecture 02 - Forbidding a Subgraph I: Mantel's Theorem and Turan's Theorem

Lecture 03 - Forbidding a Subgraph II: Complete Bipartite Subgraph

Lecture 04 - Forbidding a Subgraph III: Algebraic Constructions

Lecture 05 - Forbidding a Subgraph IV: Dependent Random Choice

Lecture 06 - Szemeredi's Graph Regularity Lemma I: Statement and Proof

Lecture 07 - Szemeredi's Graph Regularity Lemma II: Triangle Removal Lemma

Lecture 08 - Szemeredi's Graph Regularity Lemma III: Further Applications

Lecture 09 - Szemeredi's Graph Regularity Lemma IV: Induced Removal Lemma

Lecture 10 - Szemeredi's Graph Regularity Lemma V: Hypergraph Removal and Spectral Proof

Lecture 11 - Pseudo-random Graph I: Quasirandomness