The lecture notes were scribed by students who took this class and are used with their permission.

LEC # | TOPICS | LECTURE NOTES |
---|---|---|

1 | Non-Bipartite Matching: Tutte-Berge Formula, Gallai-Edmonds Decomposition, Blossoms | (PDF) by Nick Harvey (Courtesy of Nicholas Harvey. Used with permission.) |

2 | Non-Bipartite Matching: Edmonds’ Cardinality Algorithm and Proofs of Tutte-Berge Formulas and Gallai-Edmonds Decomposition | (PDF) by Robert Kleinberg (Courtesy of Robert Kleinberg. Used with permission.) |

3 | Cubic Graphs and Matchings, Factor-Critical Graphs, Ear Decompositions | (PDF) by Dan Stratila (Courtesy of Dan Stratila. Used with permission.) |

4 | The Matching Polytope, Total Dual Integrality, and Hilbert Bases | (PDF) by Constantine Caramanis |

5 |
Total Dual Integrality, Totally Unimodularity
Matching Polytope and the Cunningham-Marsh Formula Showing TDI |
(PDF) by Ben Recht (Courtesy of Benjamin Recht. Used with permission.) |

6 |
Posets and Dilworth Theorem
Deduce Konig’s Theorem for Bipartite Matchings Weighted Posets and the Chain and Antichain Polytopes |
(PDF) by Joungkeun Lim (Courtesy of Joungkeun Lim. Used with permission.) |

7 |
Partitioning Digraphs by Paths and Covering them by Cycles
Gallai-Milgram and Bessy-Thomasse Theorems Cyclic Orderings |
(PDF) by Jan Vondrák (Courtesy of Jan Vondrák. Used with permission.) |

8 |
Proof of the Bessy-Thomasse Result
The Cyclic Stable Set Polytope |
(PDF) by Constantine Caramanis (Courtesy of Constantine Caramanis. Used with permission.) |

9 | Matroids: Defs, Dual, Minor, Representability | (PDF) by Bridget Eileen Tenner (Courtesy of Bridget Tenner. Used with permission.) |

10 | Matroids: Representability, Greedy Algorithm, Matroid Polytope | (PDF) by Nicole Immorlica (Courtesy of Nicole Immorlica. Used with permission.) |

11 | Matroid Intersection | (PDF) by Fumei Lam (Courtesy of Fumei Lam. Used with permission.) |

12 | Matroid Intersection, Matroid Union, Shannon Switching Game | (PDF) by Vahab S. Mirrokni (Courtesy of Vahab Mirrokni. Used with permission.) |

13 | Matroid Intersection Polytope, Matroid Union | (PDF) by Constantine Caramanis (Courtesy of Constantine Caramanis. Used with permission.) |

14 | Matroid Union, Packing and Covering with Spanning Trees, Strong Basis Exchange Properties | (PDF) by Mohamed Mostagir (Courtesy of Mohamed Mostagir. Used with permission.) |

15 | Matroid Matching: Examples, Complexity, Lovasz’s Minmax Relation for Linear Matroids | (PDF) by Supratim Deb (Courtesy of Supratim Deb. Used with permission.) |

16 | Jump Systems: Definitions, Examples, Operations, Optimization, and Membership | (PDF) by Jonathan Kelner (Courtesy of Jonathan Kelner. Used with permission.) |

17 | Jump Systems: Membership (cont.) | |

18 | Graph Orientations, Directed Cuts (Lucchesi-Younger Theorem), Submodular Flows | (PDF) by Nick Harvey (Courtesy of Nicholas Harvey. Used with permission.) |

19 | Submodular Flows: Examples, Edmonds-Giles Theorem, Reduction to Matroid Intersection in Special Cases | (PDF) by Ben Recht (Courtesy of Benjamin Recht. Used with permission.) |

20 |
Splitting Off
$k$-Connectivity Orientations and Augmentations |
(PDF) by Jan Vondrák (Courtesy of Jan Vondrák. Used with permission.) |

21 |
Proof of Splitting-Off
Submodular Function Minimization |
(PDF) by Mohamed Mostagir (Courtesy of Mohamed Mostagir. Used with permission.) |

22 |
Multiflow and Disjoint Path Problems
Two-Commodity Flows |
(PDF) by Alantha Newman (Courtesy of Nicholas Harvey. Used with permission.) |

23 |
The Okamura-Seymour Theorem
The Wagner-Weihe Algorithm |
(PDF) by Dan Stratila |