# How to make a digraph strongly connected

@article{Frank1981HowTM, title={How to make a digraph strongly connected}, author={Andr{\'a}s Frank}, journal={Combinatorica}, year={1981}, volume={1}, pages={145-153} }

Given a directed graphG, acovering is a subsetB of edges which meets all directed cuts ofG. Equivalently, the contraction of the elements ofB makesG strongly connected. AnO(n5) primal-dual algorithm is presented for finding a minimum weight covering of an edge-weighted digraph. The algorithm also provides a constructive proof for a min-max theorem due to Lucchesi and Younger and for its weighted version.

## 63 Citations

### An improvement for an algorithm for finding a minimum feedback arc set for planar graphs

- Mathematics
- 1999

Given a directed graph G , a covering is a subset B of arcs which meets all directed cuts of G . Equivalently, the contraction of the elements of B makes G strongly connected. An O ( n 5 )…

### Preserving and Increasing Local Edge-Connectivity in Mixed Graphs

- MathematicsSIAM J. Discret. Math.
- 1995

Two splitting theorems concerning mixed graphs are proved and min-max formulae for the minimum number of new edges to be added to a mixed graph so that the resulting graph satisfies local edge-connectivity prescriptions are obtained.

### Augmenting Graphs to Meet Edge-Connectivity Requirements

- Computer ScienceFOCS
- 1990

The problem of determining the minimum number gamma of edges to be added to a graph G so that in the resulting graph the edge-connectivity between every pair (u,v) of nodes is at least a prescribed…

### Augmenting Graphs to Meet Edge-Connectivity Requirements

- MathematicsSIAM J. Discret. Math.
- 1992

A min-max formula is derived for $\gamma$ and a polynomial time algorithm to compute it is described, and the directed counterpart of the problem is solved and is shown to be NP-complete.

### An algorithm to increase the node-connectivity of a digraph by one

- MathematicsDiscret. Optim.
- 2008

### On Finding the Maximum Number of Disjoint Cuts in Seymour Graphs

- MathematicsESA
- 1999

The problem of CUT PACKING is polynomially solvable on Seymour graphs which include both all bipartite and all series-parallel graphs and it is proved that the weighted version is NP-hard even on cubic planar graphs.

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