Edge-connectivity augmentation problems
Journal of Computer and System Sciences
Computing simple circuits from a set of line segments is NP-complete
SIAM Journal on Computing
Augmenting graphs to meet edge-connectivity requirements
SIAM Journal on Discrete Mathematics
Journal of Algorithms
Augmenting edge-connectivity over the entire range in Õ(nm) time
Journal of Algorithms
A new approximation algorithm for the planar augmentation problem
Proceedings of the ninth annual ACM-SIAM symposium on Discrete algorithms
Graph connectivity and its augmentation: applications of MA orderings
Discrete Applied Mathematics
Independence free graphs and vertex connectivity augmentation
Journal of Combinatorial Theory Series B
Journal of Combinatorial Theory Series B
Augmenting the connectivity of geometric graphs
Computational Geometry: Theory and Applications
On the Hardness and Approximability of Planar Biconnectivity Augmentation
COCOON '09 Proceedings of the 15th Annual International Conference on Computing and Combinatorics
Minimum-Perimeter Polygons of Digitized Silhouettes
IEEE Transactions on Computers
Planar minimally rigid graphs and pseudo-triangulations
Computational Geometry: Theory and Applications - Special issue on the 19th annual symposium on computational geometry - SoCG 2003
Planar Biconnectivity Augmentation with Fixed Embedding
Combinatorial Algorithms
Augmenting the Connectivity of Outerplanar Graphs
Algorithmica
Augmenting undirected node-connectivity by one
Proceedings of the forty-second ACM symposium on Theory of computing
Computational Geometry: Theory and Applications
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It is shown that every connected planar straight line graph with n=3 vertices has an embedding preserving augmentation to a 2-edge connected planar straight line graph with at most @?(2n-2)/3@? new edges. It is also shown that every planar straight line tree with n=3 vertices has an embedding preserving augmentation to a 2-edge connected planar topological graph with at most @?n/2@? new edges. These bounds are the best possible. However, for every n=3, there are planar straight line trees with n vertices that do not have an embedding preserving augmentation to a 2-edge connected planar straight line graph with fewer than 1733n-O(1) new edges.