Topic: Hall's Marriage Theorem

Why Hall’s Condition Is Necessary

Translating Selection Problems Into Bipartite Graphs

Tight Hall Sets and Forced Matching Structure

The Subtraction Step in Matrix Decomposition

The Birkhoff–von Neumann Theorem

Systems of Distinct Representatives

Support Graphs of Doubly Stochastic Matrices

Strict Hall Conditions and Robust Representatives

Proving the Birkhoff–von Neumann Theorem

Positive Diagonals in Doubly Stochastic Matrices