, 
, 
such that
and either 
and 
, or
and 
.
A matching M in a graph G=(V,E) is a subset of E
such that there is no , , such that
and either and , or
and .
In other words, no node is linked to two other nodes. It's a monogamy thing.
I'll use ``green'' edges to refer to those in the matching M and ``red'' for the others.
Example...
