void graph_dfs(graph *G, vertex_t start, vertex_t* parent) {
  size_t i;

  size_t n = graph_vertex_count(G);

  bool marked[n];
  for (i = 0; i < n; ++i) {
    parent[i] = i;
    marked[i] = false;
  }
  
  marked[start] = true;
  stack* S = stack_create();
  stack_add_to_top(S, start);

  while (!stack_empty(S)) {
    // vertex_t current = top elt of S
    vertex_t current;
    stack_get_top(S, &current);
    stack_remove_top(S);

    // vertex_t neighbors[n] = neighbors of current
    size_t current_deg;
    graph_degree(G, current, &current_deg);
    vertex_t neighbors[n];
    graph_neighbors(G, current, neighbors);

    for (i = 0; i < current_deg; ++i) {
      if (!marked[neighbors[i]]) {
        marked[neighbors[i]] = true;
        parent[neighbors[i]] = current;
        stack_add_to_top(S, neighbors[i]);
      }
    }
  }
}