Comment 7 for bug 1052213

It is not a counter. You have the matching vector, and you can imagine that this vector is a big number of base |V|+1, each element of the vector is one digit. If you matched 'm' vertices so far, then you only use the first 'm' digits from the vector, the rest is assumed to be zero. Then, as the algorithm progresses, that number must increase when you are stepping down in the search tree. When you are stepping up the tree, then the number temporarily decreases, but that is fine, because you cannot step up too many times before stepping down.

So if you always make sure that stepping down increases the matching vector, then, you avoid infinite loops.

If you know what I mean, sorry, this is quite dense.