Probabilistic Methods 13-1: Large Independent Sets in Triangle Free Graphs
In the only video of Week 13 (to make up for the half week of Week 9), we state and prove the Caro-Wei Theorem on independence number. We then state and prove the theorem of Ajtai, Komlos and Szemeredi on the independence number of triangle-free graphs. Finally, we use this to prove an upper bound on the Ramsey number R(3,k).