Independence Free Graphs and Vertex Connectivity Augmentation

Authors:
Bill Jackson;Tibor Jordán
Affiliations:
-;-
Venue:
Proceedings of the 8th International IPCO Conference on Integer Programming and Combinatorial Optimization
Year:
2001

Citing 8
Cited 1

Edge-connectivity augmentation problems

Journal of Computer and System Sciences
Augmenting graphs to meet edge-connectivity requirements

SIAM Journal on Discrete Mathematics
A minimum 3-connectivity augmentation of a graph

Journal of Computer and System Sciences
On the optimal vertex-connectivity augmentation

Journal of Combinatorial Theory Series B
Minimal edge-coverings of pairs of sets

Journal of Combinatorial Theory Series B
A note on the vertex-connectivity augmentation problem

Journal of Combinatorial Theory Series B
On four-connecting a triconnected graph

Journal of Algorithms
Extremal graphs in connectivity augmentation

Journal of Graph Theory

Tight approximation algorithm for connectivity augmentation problems

ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part I

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Abstract

Given an undirected graph G and a positive integer k, the k-vertex-connectivity augmentation problem is to find a smallest set F of new edges for which G+F is k-vertex-connected. Polynomial algorithms for this problem have been found only for k ≤ 4 and a major open question in graph connectivity is whether this problem is solvable in polynomial time in general. In this paper we develop the first algorithm which delivers an optimal solution in polynomial time for every fixed k. In the case when the size of an optimal solution is large compared to k, we also give a min-max formula for the size of a smallest augmenting set. A key step in our proofs is a complete solution of the augmentation problem for a new family of graphs which we call k-independence free graphs. We also prove new splitting off theorems for vertex connectivity.