  A connected graph $G$ with at least $2m + 2n + 2$ vertices which contains a
perfect matching is $E(m, n)$-{\it extendable}, if for any two sets of disjoint
independent edges $M$ and $N$ with $|M| = m$ and $|N|= n$, there is a perfect
matching $F$ in $G$ such that $M\subseteq F$ and $N\cap F=\emptyset$.
Similarly, a connected graph with at least $n+2k+2$ vertices is called
$(n,k)$-{\it extendable} if for any vertex set $S$ of size $n$ and any matching
$M$ of size $k$ of $G-S$, $G-S-V(M)$ contains a perfect matching. Let
$\varepsilon$ be a small positive constant, $b(G)$ and $t(G)$ be the binding
number and toughness of a graph $G$. The two main theorems of this paper are:
for every graph $G$ with sufficiently large order, 1) if $b(G)\geq
4/3+\varepsilon$, then $G$ is $E(m,n)$-extendable and also $(n,k)$-extendable;
2) if $t(G)\geq 1+\varepsilon$ and $G$ has a high connectivity, then $G$ is
$E(m,n)$-extendable and also $(n,k)$-extendable. It is worth to point out that
the binding number and toughness conditions for the existence of the general
matching extension properties are almost same as that for the existence of
perfect matchings.
