How to make a digraph strongly connected

  title={How to make a digraph strongly connected},
  author={Andr{\'a}s Frank},
  • 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

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

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





Given a capacitated network with the entrance· vertex set VI and the exit-vertex set V2 on which polymatroids are defmed, an independent flow is a flow in the network such that a vector corresponding

A Minimax Theorem for Directed Graphs

This minimax equality was conjectured about a decade ago by one of the authors ([7; page 43], [8], [9]) and, independently, by Neil Robertson. It arose in the study of a problem posed several years

On two minimax theorems in graph