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 |

## Calendar

Course Info

Topics

Learning Resource Types

*notes*Lecture Notes

*assignment*Problem Sets