Instructor:
Lecture Outline:
Lecture 1 Gallai-Roy Theorem, and Gallai-Milgram Theorem. Lecture 2 Posa's Theorem on cycle partition, and Gyargas-Sarkozy Conjecture on linear cycle partition and their result on weak cycle partition. Lecture 3 Gyargas-Sarkozy Conjecture on linear cycle partition: continued. Lecture 4 Gyargas-Sarkozy Conjecture on linear cycle partition: continued. Lecture 5 k-critical graphs. Lecture 6 Alon-Krivelevich-Seymour Theorem on the longest path in k-critical graphs. Lectures 7-10 Result of Kostochka-Sudakov-Verstraete on the consecutive cycles in k-chromatic triangle-free graphs Lecture 11 Moore graphs and Benson's construction. Lecture 12 Polarity graphs. Lecture 13 Hypergraph Turan number of {C3,C4}. Lecture 14 Norm-graphs. Lecture 15 Norm-graphs: continued. Lecture 16 Turan numbers of complete bipartite graphs: an improvment. Lecture 17 Asymptotic Turan numbers of linear paths and cycles in hypergraphs. Lecture 18 Asymptotic Turan numbers of linear paths and cycles in hypergraphs: continued. Lecture 19 Asymptotic Turan numbers of linear paths and cycles in hypergraphs: completed.