Contractions, Removals and How to Certify 3-Connectivity in Linear Time
Data Structures and Algorithms
2010-11-30 v1 Discrete Mathematics
Abstract
It is well-known as an existence result that every 3-connected graph G=(V,E) on more than 4 vertices admits a sequence of contractions and a sequence of removal operations to K_4 such that every intermediate graph is 3-connected. We show that both sequences can be computed in optimal time, improving the previously best known running times of O(|V|^2) to O(|V|+|E|). This settles also the open question of finding a linear time 3-connectivity test that is certifying and extends to a certifying 3-edge-connectivity test in the same time. The certificates used are easy to verify in time O(|E|).
Cite
@article{arxiv.1011.6187,
title = {Contractions, Removals and How to Certify 3-Connectivity in Linear Time},
author = {Jens M. Schmidt},
journal= {arXiv preprint arXiv:1011.6187},
year = {2010}
}
Comments
preliminary version