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Matchings

Learn to identify different types of matchings within graphs, including maximum and perfect matchings. Understand how maximum matchings apply to bipartite graphs for practical uses such as assigning resources to tasks. This lesson helps clarify key terms and concepts essential for solving matching problems in graph theory.

Matchings and related terminology

A matching MM of an undirected graph GG is any collection of its edges that have no end-vertex in common. In other words, each edge in MM uniquely pairs or matches two vertices. We refer to the number of edges in a matching MM as the size of the matching MM.

If a vertex appears as an end-vertex of an edge in ...