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Topics in Structural Graph Theory by Ortrud R. Oellermann, Robin J. Wilson, Lowell W. Beineke

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12

Connectivity algorithms

ABDOL-HOSSEIN ESFAHANIAN

1   Introduction

2   Computing the edge-connectivity

3   Computing the arc-connectivity

4   Computing the vertex-connectivity

5   Concluding remarks

References

This chapter presents an exposition of how connectivity algorithms have advanced over the years. Most of these algorithms work by making a number of calls to a max-flow subroutine. As these calls determine the bulk of the computation, attempts have been made to minimize the number of such calls.

1. Introduction

A variety of algorithms for the computation of the vertex-connectivity κ(G) and the edge-connectivity λ(G) of a graph G have been developed over the years. Most of these algorithms work by solving a number of maximum-flow problems ...

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