Maintenance of Triconnected Components of Graphs (Extended Abstract)

In this paper, optimal algorithms and data structures are presented to maintain the triconnected components of a general graph, under insertions of edges in the graph. At any moment, the data structure can answer the following type of query: given two nodes in the graph, are these nodes triconnected. Starting from an “empty” graph of n nodes (i.e., a graph with no edges) the solution runs in O(n + m.α(m, n)) total time, where m is the total number of queries and edge insertions. The solution allows for insertions of nodes also.

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