Algorithmica

, Volume 7, Issue 1–6, pp 583–596

A linear-time algorithm for finding a sparsek-connected spanning subgraph of ak-connected graph

  • Hiroshi Nagamochi
  • Toshihide Ibaraki
Article

DOI: 10.1007/BF01758778

Cite this article as:
Nagamochi, H. & Ibaraki, T. Algorithmica (1992) 7: 583. doi:10.1007/BF01758778

Abstract

We show that anyk-connected graphG = (V, E) has a sparsek-connected spanning subgraphG′ = (V, E′) with ¦E′¦ =O(k¦V¦) by presenting anOE¦)-time algorithm to find one such subgraph, where connectivity stands for either edge-connectivity or node-connectivity. By using this algorithm as preprocessing, the time complexities of some graph problems related to connectivity can be improved. For example, the current best time boundO(max{k2¦V¦1/2,k¦V¦}¦E¦) to determine whether node-connectivityK(G) of a graphG = (V, E) is larger than a given integerk or not can be reduced toO(max{k3¦V¦3/2,k2¦V¦2}).

Key words

Undirected graphs Spanning subgraphs Connectivity k-edge-connectivity k-node-connectivity Linear-time algorithms 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer-Verlag New York Inc. 1992

Authors and Affiliations

  • Hiroshi Nagamochi
    • 1
  • Toshihide Ibaraki
    • 1
  1. 1.Department of Applied “Mathematics and Physics, Faculty of EngineeringKyoto UniversityKyotoJapan

Personalised recommendations