# 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}
}
• A. Frank
• Published 1 June 1981
• Mathematics, Computer Science
• Combinatorica
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.

### 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

• Mathematics
SIAM 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

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

• A. Frank
• Mathematics
SIAM 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.

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

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.

### Tree-compositions and orientations

• Computer Science, Mathematics
Oper. Res. Lett.
• 2013