A simple certifying algorithm for 3-edge-connectivity
Abstract
A linear-time certifying algorithm for 3-edge-connectivity is presented. Given an undirected graph G, if G is 3-edge-connected, the algorithm generates a construction sequence as a positive certificate for G. Otherwise, the algorithm decomposes G into its 3-edge-connected components and at the same time generates a construction sequence for each connected component as well as the bridges and a cactus representation of the cut-pairs in G. All of these are done by making only one pass over G using an innovative graph contraction technique. Moreover, the graph need not be 2-edge-connected.
Cite
@article{arxiv.2002.04727,
title = {A simple certifying algorithm for 3-edge-connectivity},
author = {Yung H. Tsin},
journal= {arXiv preprint arXiv:2002.04727},
year = {2022}
}
Comments
Section 3.2 has been rewritten to improve clarity. In Section 3.3, the correctness proof is elaborated. Figures 5 and 8 are shifted to the end as an appendix. Their captions are more detailed