Check Your Understanding

Before moving on, test your understanding. If node $u$ is an ancestor of node $v$, what is true about their entry and exit times?

Answer: tin[u] < tin[v] and tout[u] > tout[v]. The ancestor enters first and exits last. This property is the foundation for checking if one node is in another's subtree. If tin[u] <= tin[v] and tout[v] <= tout[u], then $v$ is in $u$'s subtree. You will use this check constantly when working with Euler tours.