On the optimal vertex-connectivity augmentation
Journal of Combinatorial Theory Series B
Fast algorithms for k-shredders and k-node connectivity augmentation (extended abstract)
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
A note on the vertex-connectivity augmentation problem
Journal of Combinatorial Theory Series B
Optimal augmentation to make a graph k-edge-connected and triconnected
Proceedings of the ninth annual ACM-SIAM symposium on Discrete algorithms
Augmenting Edge and Vertex Connectivities Simultaneously
ISAAC '97 Proceedings of the 8th International Symposium on Algorithms and Computation
K-Edge and 3-Vertex Connectivity Augmentation in an Arbitrary Multigraph
ISAAC '98 Proceedings of the 9th International Symposium on Algorithms and Computation
Undirected Vertex-Connectivity Structure and Smallest Four-Vertex-Connectivity Augmentation
ISAAC '95 Proceedings of the 6th International Symposium on Algorithms and Computation
Optimal Bi-Level Augmentation for Selectivity Enhancing Graph Connectivity with Applications
COCOON '96 Proceedings of the Second Annual International Conference on Computing and Combinatorics
Edge-Connectivity Augmentation Preserving Simplicity
FOCS '97 Proceedings of the 38th Annual Symposium on Foundations of Computer Science
On the Minimum Augmentation of an l-Connected Graph to a k-Connected Graph
SWAT '00 Proceedings of the 7th Scandinavian Workshop on Algorithm Theory
Simultaneous Augmentation of Two Graphs to an l-Edge-Connected Graph and a Biconnected Graph
ISAAC '00 Proceedings of the 11th International Conference on Algorithms and Computation
Graph connectivity and its augmentation: applications of MA orderings
Discrete Applied Mathematics
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Given an undirected multigraph G = (V,E) and two positive integers l and k, we consider the problem of augmenting G by the smallest number of new edges to obtain an l-edge-connected and k-vertex-connected multigraph. In this paper, we show that an (k - 1)-vertex-connected multigraph G (k 驴 4) can be made l-edge-connected and k-vertex-connected by adding at most 2l surplus edges over the optimum, in O(min{k,驴n}kn3 + n4) time, where n = |V|.