Certifying 3-Edge-Connectivity
Data Structures and Algorithms
2015-10-08 v3 Discrete Mathematics
Abstract
We present a certifying algorithm that tests graphs for 3-edge-connectivity; the algorithm works in linear time. If the input graph is not 3-edge-connected, the algorithm returns a 2-edge-cut. If it is 3-edge-connected, it returns a construction sequence that constructs the input graph from the graph with two vertices and three parallel edges using only operations that (obviously) preserve 3-edge-connectivity. Additionally, we show how compute and certify the 3-edge-connected components and a cactus representation of the 2-cuts in linear time. For 3-vertex-connectivity, we show how to compute the 3-vertex-connected components of a 2-connected graph.
Cite
@article{arxiv.1211.6553,
title = {Certifying 3-Edge-Connectivity},
author = {Kurt Mehlhorn and Adrian Neumann and Jens M. Schmidt},
journal= {arXiv preprint arXiv:1211.6553},
year = {2015}
}
Comments
29 pages in Algorithmica, 2015