A linear time algorithm for minimum augmentation to 3-connect specified vertices of a graph
Toshiya Mashima, Takuo Watanabe · 2002
The subject of the paper is the 3-vertex-connectivity augmentation problem for a specified set of vertices (3VCA-SV), which is defined as follows: given an undirected graph G=(V, E) and a specified subset S of V with |S|>3, find a smallest set of edges to be added to G so that the resulting graph may have the property that, even after deleting any two vertices from it, there is a path between any pair of remaining vertices in S. The result of the paper is that 3VCA-SV can be solved optimally in linear time.