A Characterization of Separating Pairs and Triplets in a Graph.

Abstract : Connectivity is an important graph property and there has been a considerable amount of work on algorithms for determining connectivity of graphs. An undirected graph G =(V,E) is k-connected if for any subset V' of k-1 vertices of G the subgraph induced by V-V' is connected. A subset V' of k vertices is a separating k-set if the subgraph induced by V-V' is not connected. For k=1 the set V' becomes a single vertex which is called an articulation point, and for k=2,3 the set V' is called a separating pair and separating triplet, respectively. Efficient algorithms are available for finding all separating k-sets in k-connected undirected graphs for k or = 3. The authors address the following question: what is the maximum number of separating pairs and triplets in biconnected and triconnected undirected graphs, respectively?

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