1 
NonBipartite Matching: TutteBerge Formula, GallaiEdmonds Decomposition, Blossoms 
(PDF) by Nick Harvey (Courtesy of Nicholas Harvey. Used with permission.) 
2 
NonBipartite Matching: Edmonds' Cardinality Algorithm and Proofs of TutteBerge Formulas and GallaiEdmonds Decomposition 
(PDF) by Robert Kleinberg (Courtesy of Robert Kleinberg. Used with permission.) 
3 
Cubic Graphs and Matchings, FactorCritical 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 CunninghamMarsh 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
GallaiMilgram and BessyThomasse Theorems
Cyclic Orderings 
(PDF) by Jan Vondrák (Courtesy of Jan Vondrák. Used with permission.) 
8 
Proof of the BessyThomasse 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 (LucchesiYounger Theorem), Submodular Flows 
(PDF) by Nick Harvey (Courtesy of Nicholas Harvey. Used with permission.) 
19 
Submodular Flows: Examples, EdmondsGiles 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 SplittingOff
Submodular Function Minimization 
(PDF) by Mohamed Mostagir (Courtesy of Mohamed Mostagir. Used with permission.) 
22 
Multiflow and Disjoint Path Problems
TwoCommodity Flows 
(PDF) by Alantha Newman (Courtesy of Nicholas Harvey. Used with permission.) 
23 
The OkamuraSeymour Theorem
The WagnerWeihe Algorithm 
(PDF) by Dan Stratila 