Understanding maximum bipartite matching problem

A bipartite graph is a graph whose nodes can be divided into two disjoint sets, L and R, so all edges connect nodes from one set to another. Bipartite graphs arise naturally when we try to model relationships between two different classes of objects, and their structured nature allows us to model many real-life problems using them. They are most commonly used in optimization problems where we want to maximize fixed resource usage among some users.

Now that we know what a bipartite graph is let's look at some terminologies to help us understand the maximum bipartite matching problem.