A perfect matching in graph theory is a special type of matching where every vertex in a graph is connected to exactly one other vertex. This means that all vertices are paired up without any left out, creating a complete set of connections. Perfect matchings are often found in bipartite graphs, where the vertices can be divided into two distinct sets. In practical applications, perfect matchings can be used in various fields, such as network design, scheduling problems, and resource allocation. Finding a perfect matching can help optimize connections and ensure that resources are efficiently distributed among participants or tasks.