Maintenance of triconnected components of graphs

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, axe 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.