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Encyclopedia of Algorithms pp 797–800Cite as

Fully Dynamic Higher Connectivity

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  • First Online:

Years and Authors of Summarized Original Work

  • 1997; Eppstein, Galil, Italiano, Nissenzweig

Problem Definition

The problem is concerned with efficiently maintaining information about edge and vertex connectivity in a dynamically changing graph. Before defining formally the problems, a few preliminary definitions follow.

Given an undirected graph \( { G=(V,E) } \), and an integer \( { k\geq 2 } \), a pair of vertices \( { \langle u,v\rangle } \) is said to be k-edge‐connected if the removal of any \( { (k-1) } \) edges in G leaves u and v connected. It is not difficult to see that this is an equivalence relationship: the vertices of a graph G are partitioned by this relationship into equivalence classes called k-edge‐connected components. G is said to be k-edge‐connected if the removal of any \( { (k-1) } \) edges leaves G connected. As a result of these definitions, G is k-edge‐connected if and only if any two vertices of G are k-edge‐connected. An edge set \( { E^{\prime}\subseteq E }...

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Author information

Authors and Affiliations

  1. Department of Computer and Systems Science, University of Rome, Rome, Italy

    Giuseppe F. Italiano

  2. Department of Information and Computer Systems, University of Rome, Rome, Italy

    Giuseppe F. Italiano

Authors
  1. Giuseppe F. Italiano
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Editor information

Editors and Affiliations

  1. Department of Electrical Engineering and Computer Science, Northwestern University, Evanston, IL, USA

    Ming-Yang Kao

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Italiano, G. (2016). Fully Dynamic Higher Connectivity. In: Kao, MY. (eds) Encyclopedia of Algorithms. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-2864-4_154

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