Edge-connectivity augmentation problems
Journal of Computer and System Sciences
A linear time algorithm for triconnectivity augmentation (extended abstract)
SFCS '91 Proceedings of the 32nd annual symposium on Foundations of computer science
Augmenting graphs to meet edge-connectivity requirements
SIAM Journal on Discrete Mathematics
Finding a smallest augmentation to biconnect a graph
SIAM Journal on Computing
Minimal edge-coverings of pairs of sets
Journal of Combinatorial Theory Series B
On four-connecting a triconnected graph
Journal of Algorithms
Simpler and faster biconnectivity augmentation
Journal of Algorithms
Independence free graphs and vertex connectivity augmentation
Journal of Combinatorial Theory Series B
Augmenting undirected node-connectivity by one
Proceedings of the forty-second ACM symposium on Theory of computing
Hi-index | 0.00 |
For a connected graph, a subset of vertices of least size whose deletion increases the number of connected components is the vertex connectivity of the graph. A graph with vertex connectivity k is said to be k-vertex connected. Given a k-vertex connected graph G, vertex connectivity augmentation determines a smallest set of edges whose augmentation to G makes it (k + 1)-vertex connected. In this paper, we report our study of connectivity augmentation in 1-connected graphs, 2-connected graphs, and k-trees. For a graph, our data structure maintains the set of equivalence classes based on an equivalence relation on the set of leaves of an associated tree. This partition determines a set of edges to be augmented to increase the connectivity of the graph by one. Based on our data structure we present a new combinatorial analysis and an elegant proof of correctness of our linear time algorithm for optimum connectivity augmentation. While this is the first attempt on the study of k-tree augmentation, the study on other two augmentations is reported in the literature. Compared to other augmentations reported in the literature, we avoid recomputation of the associated tree by maintaining the data structure under edge additions.