A new graphy triconnectivity algorithm and its parallelization
STOC '87 Proceedings of the nineteenth annual ACM symposium on Theory of computing
Reducing edge connectivity to vertex connectivity
ACM SIGACT News
A linear time algorithm for triconnectivity augmentation (extended abstract)
SFCS '91 Proceedings of the 32nd annual symposium on Foundations of computer science
Finding triconnected components by local replacement
SIAM Journal on Computing
Maintaining the 3-edge-connected components of a graph on-line
SIAM Journal on Computing
Journal of the ACM (JACM)
Path-based depth-first search for strong and biconnected components
Information Processing Letters
Maintenance of Triconnected Components of Graphs (Extended Abstract)
ICALP '92 Proceedings of the 19th International Colloquium on Automata, Languages and Programming
A Linear Time Implementation of SPQR-Trees
GD '00 Proceedings of the 8th International Symposium on Graph Drawing
Graph Theory With Applications
Graph Theory With Applications
A Simple 3-Edge-Connected Component Algorithm
Theory of Computing Systems
Yet another optimal algorithm for 3-edge-connectivity
Journal of Discrete Algorithms
Graphs, Networks and Algorithms
Graphs, Networks and Algorithms
Hybrid Graph Theory and Network Analysis
Hybrid Graph Theory and Network Analysis
Decomposing a multigraph into split components
CATS '12 Proceedings of the Eighteenth Computing: The Australasian Theory Symposium - Volume 128
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Vertex-connectivity and edge-connectivity represent the extent to which a graph is connected. Study of these key properties of graphs plays an important role in varieties of computer science applications. Recent years have witnessed a number of linear time 3-edge-connectivity algorithms - with increasing simplicity. In contrast, the state-of-the-art algorithm for 3-vertex-connectivity due to Hopcroft and Tarjan lacks the simplicity in the sense of ease of implementation as well as the number of passes over the graph although its time and space complexity is theoretically linear. In this paper, we propose a linear time reduction from 3-vertex-connectivity to 3-edge-connectivity of a multigraph. This reduction was previously unknown, while the reduction in the opposite direction already exists. We apply an existing linear time 3-edge-connectivity algorithm on the reduced graph for solving the 3-vertex-connectivity of the original graph. Hence, for a graph with |V| vertices and |E| edges, the proposed reduction turns into an O(|V| + |E|) time and space algorithm for 3-vertex-connectivity while enjoying the simplicity of the 3-edge-connectivity algorithms.