A smallest augmentation to 3-connect a graph
Discrete Applied Mathematics
Faster scaling algorithms for general graph matching problems
Journal of the ACM (JACM)
A linear time algorithm for triconnectivity augmentation (extended abstract)
SFCS '91 Proceedings of the 32nd annual symposium on Foundations of computer science
Pfaffian forms and &Dgr;-matroids
Discrete Mathematics
Finding a smallest augmentation to biconnect a graph
SIAM Journal on Computing
On the optimal vertex-connectivity augmentation
Journal of Combinatorial Theory Series B
Delta-Matroids, Jump Systems, and Bisubmodular Polyhedra
SIAM Journal on Discrete Mathematics
Minimal edge-coverings of pairs of sets
Journal of Combinatorial Theory Series B
The membership problem in jump systems
Journal of Combinatorial Theory Series B - Special issue: dedicated to Professor W. T. Tutte on the occasion of his eightieth birthday
A note on the vertex-connectivity augmentation problem
Journal of Combinatorial Theory Series B
Data structures for weighted matching and nearest common ancestors with linking
SODA '90 Proceedings of the first annual ACM-SIAM symposium on Discrete algorithms
On four-connecting a triconnected graph
Journal of Algorithms
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
Undirected Vertex-Connectivity Structure and Smallest Four-Vertex-Connectivity Augmentation
ISAAC '95 Proceedings of the 6th International Symposium on Algorithms and Computation
A Near Optimal Algorithm for Vertex Connectivity Augmentation
ISAAC '00 Proceedings of the 11th International Conference on Algorithms and Computation
Restricted t-matchings in bipartite graphs
Discrete Applied Mathematics - Submodularity
Maximum skew-symmetric flows and matchings
Mathematical Programming: Series A and B
Independence free graphs and vertex connectivity augmentation
Journal of Combinatorial Theory Series B
M-Convex Functions on Jump Systems: A General Framework for Minsquare Graph Factor Problem
SIAM Journal on Discrete Mathematics
Finding maximum square-free 2-matchings in bipartite graphs
Journal of Combinatorial Theory Series B
A Steepest Descent Algorithm for M-Convex Functions on Jump Systems
IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
On shredders and vertex connectivity augmentation
Journal of Discrete Algorithms
Combinatorial algorithms for matchings, even factors and square-free 2-factors
Mathematical Programming: Series A and B
Operations on M-Convex Functions on Jump Systems
SIAM Journal on Discrete Mathematics
On Maximum Cost $K_{t,t}$-Free $t$-Matchings of Bipartite Graphs
SIAM Journal on Discrete Mathematics
Polynomial-Time Algorithms for Linear and Convex Optimization on Jump Systems
SIAM Journal on Discrete Mathematics
Primal-dual approach for directed vertex connectivity augmentation and generalizations
ACM Transactions on Algorithms (TALG)
Even factors, jump systems, and discrete convexity
Journal of Combinatorial Theory Series B
A Weighted kt, t-Free t-Factor Algorithm for Bipartite Graphs
Mathematics of Operations Research
Augmenting undirected node-connectivity by one
Proceedings of the forty-second ACM symposium on Theory of computing
A proof of Cunningham's conjecture on restricted subgraphs and jump systems
Journal of Combinatorial Theory Series B
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We consider the problem of making a given (k-1)-connected graph k-connected by adding a minimum number of new edges, which we call the k-connectivity augmentation problem. In this paper, we deal with the problem when k=n-3 where n is the number of vertices of the input graph. By considering the complement graph, the (n-3)-connectivity augmentation problem can be reduced to the problem of finding a maximum square-free 2-matching in a simple graph with maximum degree at most three. We give a polynomial-time algorithm to find a maximum square-free 2-matching in a simple graph with maximum degree at most three, which yields a polynomial-time algorithm for the (n-3)-connectivity augmentation problem. Our algorithm is based on the fact that the square-free 2-matchings are endowed with a matroid structure called a jump system. We also show that the weighted (n-3)-connectivity augmentation problem can be solved in polynomial time if the weights are induced by a function on the vertex set, whereas the problem is NP-hard for general weights.