The exhaustive list of topics in Combinatorial Optimization in which we provide Help with Homework Assignment and Help with Project is as follows:
- Non-Bipartite Matching: Tutte-Berge Formula, Gallai-Edmonds Decomposition, Blossoms
- Non-Bipartite Matching: Edmonds' Cardinality Algorithm and Proofs of Tutte-Berge Formulas and Gallai-Edmonds Decomposition
- Cubic Graphs and Matchings, Factor-Critical Graphs, Ear Decompositions
- Matching Polytope, Total Dual Integrality, and Hilbert Bases
- Total Dual Integrality
- Totally Unimodularity
- Matching Polytope and the Cunningham-Marsh Formula Showing TDI
- Posets and Dilworth Theorem
- Deduce Konig's Theorem for Bipartite Matchings
- Weighted Posets and the Chain and Antichain Polytopes
- Partitioning Digraphs by Paths and Covering them by Cycles
- Gallai-Milgram and Bessy-Thomasse Theorems
- Cyclic Orderings
- Proof of the Bessy-Thomasse Result
- Cyclic Stable Set Polytope
- Matroids: Dual, Minor, Representability
- Matroids: Representability, Greedy Algorithm, Matroid Polytope
- Matroid Intersection
- Matroid Union, Shannon Switching Game
- Matroid Intersection Polytope, Matroid Union
- Matroid Union, Packing and Covering with Spanning Trees, Strong Basis Exchange Properties
- Matroid Matching: Examples, Complexity, Lovasz's Minmax Relation for Linear Matroids
- Graph Orientations, Directed Cuts (Lucchesi-Younger Theorem), Submodular Flows
- Submodular Flows: Examples, Edmonds-Giles Theorem, Reduction to Matroid Intersection in Special Cases
- Connectivity Orientations and Augmentations
- Splitting Off
- Proof of Splitting-Off
- Submodular Function Minimization
- Multiflow and Disjoint Path Problems
- Two-Commodity Flows
- Okamura-Seymour Theorem and the Wagner-Weihe Linear-Time Algorithm