On-Line Graph Algorithms with SPQR-Trees

We present the SPQR-tree, a versatile data structure that represents the decomposition of a biconnected graph with respect to its triconnected components, and show its application to a variety of on-line graph algorithms dealing with triconnectivity, transitive closure, minimum spanning tree, and planarity testing. The results are further extended to general graphs by means of another data structure, the BC-tree.

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