Maximally matchable edge

In the context of graph theory, particularly when discussing matchings in bipartite graphs, a **maximally matchable edge** refers to an edge in a matching that cannot be included in a larger matching without violating the properties of disjointness. ### Key Concepts: 1. **Matching**: A matching in a graph is a set of edges without common vertices. A perfect matching is a matching that covers every vertex of the graph. 2. **Maximal Matching vs.