2-Vertex Connectivity in Directed Graphs
Abstract
We complement our study of 2-connectivity in directed graphs, by considering the computation of the following 2-vertex-connectivity relations: We say that two vertices v and w are 2-vertex-connected if there are two internally vertex-disjoint paths from v to w and two internally vertex-disjoint paths from w to v. We also say that v and w are vertex-resilient if the removal of any vertex different from v and w leaves v and w in the same strongly connected component. We show how to compute the above relations in linear time so that we can report in constant time if two vertices are 2-vertex-connected or if they are vertex-resilient. We also show how to compute in linear time a sparse certificate for these relations, i.e., a subgraph of the input graph that has O(n) edges and maintains the same 2-vertex-connectivity and vertex-resilience relations as the input graph, where n is the number of vertices.
Keywords
Cite
@article{arxiv.1409.6277,
title = {2-Vertex Connectivity in Directed Graphs},
author = {Loukas Georgiadis and Giuseppe F. Italiano and Luigi Laura and Nikos Parotsidis},
journal= {arXiv preprint arXiv:1409.6277},
year = {2015}
}
Comments
arXiv admin note: substantial text overlap with arXiv:1407.3041