Articulation Points (Tarjan)

Robert Tarjan, 1972

Tarjan’s 1972 lowlink framework extends bridge detection: a non-root vertex is articulating when some DFS child cannot reach an ancestor (low[child] ≥ disc[v]), and the root qualifies only with two independent subtrees. This gallery piece animates a seven-vertex construction—triangle fused to a bridge tail—so gold traces the active DFS frame, ochre edges mark tentative neighbor scans, stone edges stay quiet, and coral isolates the final articulation set while teal epilogues echo the finished traversal.