optimization in brute force vertex cover algorithm

Question

I'm writing a brute-force algorithm to solve vertex cover like this:

BruteForceVertexCover( Graph G = (V,E) ){
    for size= 1 ... |V|
        vector<int> v = {0...size-1}
        do{
            if(test(G, v)) return v;     //test if v covers G
        }
        while(v has next combinations of lenght size);
    return empty vector<int>;
}

//this stops when find a answer, and it will find,
//since it tries all combinations of all sizes

where

bool test( Graph G = (V,E), vector<int> v ){
    for each u in v:
        for each w in G[u]
            remove u from G[w]     //this is linear in size of vector G[w]
        clear G[v]                 //removed all (bidirectional) edges that have u
    for i = 0 ... |V|
        if(G[i] is not empty) return false;
        return true;
}

im trying this to lots of graphs (but their maximum size is 20 vertices) and this is taking a decade... is there any optimization I can do on this brute force so it run faster?