# Matchings

Learn about graph matchings.

## We'll cover the following

## Matchings and related terminology

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

If a vertex appears as an end-vertex of an edge in $M$, we say it is **matched** by $M$. Otherwise, we say it is **unmatched** by $M$. Some examples of matchings in graphs are shown in the set of slides below.

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