Augmenting undirected node-connectivity by one

Graph Theory Seminar
Thursday, March 8, 2012 - 12:05
1 hour (actually 50 minutes)
Skiles 005
In the node-connectivity augmentation problem, we want to add a minimum number of new edges to an undirected graph to make it k-node-connected. The complexity of this question is still open, although the analogous questions of both directed and undirected edge-connectivity and directed node-connectivity augmentation are known to be polynomially solvable. I present a min-max formula and a polynomial time algorithm for the special case when the input graph is already (k-1)-connected. The formula has been conjectured by Frank and Jordan in 1994. In the first lecture, I shall investigate the background, present some results on the previously solved connectivity augmentation cases, and exhibit examples motivating the complicated min-max formula of my paper.