Instead of storing the full tour, store two timestamps per node: when you enter it (tin[v]) and when you exit it (tout[v]). Run DFS with a global timer. When you first visit node , set tin[v] = timer and increment timer.
After visiting all children, set tout[v] = timer (without incrementing). Now every node has a time interval [tin[v], tout[v]] that represents when DFS was inside that subtree.