research-article

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

Authors:

Hiroshi Nagamochi,

Toshihide IbarakiAuthors Info & Claims

Algorithmica, Volume 7, Issue 1-6

Pages 583 - 596

https://doi.org/10.1007/BF01758778

Published: 22 March 2023 Publication History

Abstract

We show that anyk-connected graphG = (V, E) has a sparsek-connected spanning subgraphG′ = (V, E′) with ¦E′¦ =O(k¦V¦) by presenting anO(¦E¦)-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}).

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Published In

Algorithmica Volume 7, Issue 1-6

Jun 1992

628 pages

ISSN:0178-4617

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Publisher

Springer-Verlag

Berlin, Heidelberg

Publication History

Published: 22 March 2023

Revision received: 16 August 1990

Received: 06 September 1989

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