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Revision difference : matching
Version current Version 3
Let $G$ be a graph. A \emph{matching} $M$ on $G$ is a subset of the edges of $G$ such that each vertex in $G$ is incident with no more than one edge in $M$. Let $G$ be a graph. A \emph{matching} $M$ on $G$ is a subset of the edges of $G$ such that each vertex in $G$ is incident with no more than one edge in $M$.
It is easy to find a matching on a graph; for example, the empty set will always be a matching. Typically, the most interesting matchings are \emph{maximal matchings}. A maximal matching on a graph $G$ is simply a matching of the largest possible size. It is easy to find a matching on a graph; for example, the empty set will always be a matching. Typically, the most interesting matchings are \emph{maximal matchings}. A maximal matching on a graph $G$ is simply a matching of the largest possible size.
A \emph{perfect matching} is a matching that saturates every vertex.