| LEC # | TOPICS |
|---|---|
| 1 | Non-Bipartite Matching: Tutte-Berge Formula, Gallai-Edmonds Decomposition, Blossoms |
| 2 | Non-Bipartite Matching: Edmonds' Cardinality Algorithm and Proofs of Tutte-Berge Formulas and Gallai-Edmonds Decomposition |
| 3 | Cubic Graphs and Matchings, Factor-Critical Graphs, Ear Decompositions |
| 4 | The Matching Polytope, Total Dual Integrality, and Hilbert Bases |
| 5 | Total Dual Integrality, Totally Unimodularity Matching Polytope and the Cunningham-Marsh Formula Showing TDI |
| 6 | Posets and Dilworth Theorem Deduce Konig's Theorem for Bipartite Matchings Weighted Posets and the Chain and Antichain Polytopes |
| 7 | Partitioning Digraphs by Paths and Covering them by Cycles Gallai-Milgram and Bessy-Thomasse Theorems Cyclic Orderings |
| 8 | Proof of the Bessy-Thomasse Result The Cyclic Stable Set Polytope |
| 9 | Matroids: Defs, Dual, Minor, Representability |
| 10 | Matroids: Representability, Greedy Algorithm, Matroid Polytope |
| 11 | Matroid Intersection |
| 12 | Matroid Intersection, Matroid Union, Shannon Switching Game |
| 13 | Matroid Intersection Polytope, Matroid Union |
| 14 | Matroid Union, Packing and Covering with Spanning Trees, Strong Basis Exchange Properties |
| 15 | Matroid Matching: Examples, Complexity, Lovasz's Minmax Relation for Linear Matroids |
| 16 | Jump Systems: Definitions, Examples, Operations, Optimization, and Membership |
| 17 | Jump Systems: Membership (cont.) |
| 18 | Graph Orientations, Directed Cuts (Lucchesi-Younger Theorem), Submodular Flows |
| 19 | Submodular Flows: Examples, Edmonds-Giles Theorem, Reduction to Matroid Intersection in Special Cases |
| 20 | Splitting Off $k$-Connectivity Orientations and Augmentations |
| 21 | Proof of Splitting-Off Submodular Function Minimization |
| 22 | Multiflow and Disjoint Path Problems Two-Commodity Flows |
| 23 | The Okamura-Seymour Theorem and the Wagner-Weihe Linear-Time Algorithm |