Given a biconnected graph G = (V,E) with edge s, t ∈ E, an st-ordering is an ordering v1, . . . , vn of V such that s = v1, t = vn, and every other vertex has both a higher-numbered and a lower-numbered neighbor. Previous linear-time st-ordering algorithms are based on a preprocessing step in which depth-first search is used to compute lowpoints. The actual ordering is determined only in a second pass over the graph. We present a new, incremental algorithm that does not require lowpoint information and, throughout a single depth-first traversal, maintains an st-ordering of the biconnected component of s, t in the traversed subgraph.
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- A. Lempel, S. Even, and I. Cederbaum. An algorithm for planarity testing of graphs. In P. Rosenstiehl, editor, Proceedings of the International Symposium on the Theory of Graphs (Rome, July 1966), pages 215–232. Gordon and Breach, 1967.Google Scholar