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Joined 2026-09-21 Message
Incoming links: DFS discovery and finishing times
Maintain white, gray and black colors for undiscovered, active and completed vertices. A single traversal clock records DFS discovery and finishing times:
for v in V: color[v] = white; parent[v] = none
time = 0
visit(u):
time = time+1; d[u] = time; color[u] = gray
for v in adjacency[u]:
if color[v] == white:
parent[v] = u
visit(v)
color[u] = black; time = time+1; f[u] = time
for u in V:
if color[u] == white: visit(u)The outer loop makes a depth-first search forest even when the directed graph is disconnected. Each vertex is entered once and each directed adjacency entry is inspected once. Thus an adjacency list representation gives time and auxiliary storage, including the worst-case recursive stack. Sorting neighbors to impose a particular visit order would be additional work.
Increment a single clock on each discovery and finish, starting with clock zero. Lexicographic depth-first search givesThe first search tree has discovery edges , , . The edge returns to an active ancestor. Once that tree finishes, vertex is a new root whose neighbour is already finished, and vertex is the final root. This accounts for all twelve events in the DFS discovery and finishing times.