 Matching number

For a finite graph $G$, the matching number isIt is the cardinality of a maximum cardinality matching. The vertex capacity constraint gives $0\le \nu (G)\le \lfloor |V(G)|/2\rfloor$. 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.