Matching number
= Matching number
{title2=$\nu(G)$}
= Maximum matching number
{synonym}
For a finite <graph> $G$, the <matching number> is
$$
\nu(G)=\max\{|M|:M\text{ is a matching of }G\}.
$$
It is the <cardinality> of a <maximum cardinality matching>. The vertex capacity constraint gives $0\leq\nu(G)\leq\lfloor |V(G)|/2\rfloor$. The worked <path graph> examples have $\nu(P_4)=2$ and $\nu(P_6)=3$. A <perfect matching> reaches $|V(G)|/2$; the empty <graph> has <matching number> zero.