| 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 |