Euler Tour - Construction

Here's how to build the Euler tour:

function eulerTour(root)
    timer := 0
    dfs(root, -1)

function dfs(v, parent)
    tin[v] := timer
    timer := timer + 1
    tour[tin[v]] := v

    for each child u of v (u ≠ parent)
        dfs(u, v)

    tout[v] := timer - 1

The tour array stores nodes in DFS order. For subtree of $v$, indices $[tin[v], tout[v]]$ contain exactly the nodes in $v$'s subtree.