Perfect Matching

A perfect matching is a way to pair up elements in two groups so that every element in each group is matched with exactly one element from the other group, with no leftovers. Imagine a set of people and a set of tasks, and each person can do only one task. A perfect matching assigns each person to a unique task they can perform, ensuring all people and tasks are paired with no gaps. It’s a key concept in graph theory used to solve problems where complete, one-to-one pairings are needed.