Abstract
A directed graph G = (V,E) is twinless strongly connected if it contains a strongly connected spanning subgraph without any pair of antiparallel (or twin) edges. The twinless strongly connected components (TSCCs) of a directed graph G are its maximal twinless strongly connected subgraphs. These concepts have several diverse applications, such as the design of telecommunication networks and the structural stability of buildings. A vertex v ∈ V is a twinless strong articulation point of G, if the deletion of v increases the number of TSCCs of G. Here, we present the first lineartime algorithm that finds all the twinless strong articulation points of a directed graph. We show that the computation of twinless strong articulation points reduces to the following problem in undirected graphs, which may be of independent interest: Given a 2vertexconnected undirected graph H, find all vertices v for which there exists an edge e such that H⧵{v,e} is not connected. We develop a lineartime algorithm that not only finds all such vertices v, but also computes the number of edges e such that H⧵{v,e} is not connected. This also implies that for each twinless strong articulation point v which is not a strong articulation point in a strongly connected digraph G, we can compute the number of TSCCs in G⧵v.
BibTeX  Entry
@InProceedings{georgiadis_et_al:LIPIcs:2020:13382,
author = {Loukas Georgiadis and Evangelos Kosinas},
title = {{LinearTime Algorithms for Computing Twinless Strong Articulation Points and Related Problems}},
booktitle = {31st International Symposium on Algorithms and Computation (ISAAC 2020)},
pages = {38:138:16},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {9783959771733},
ISSN = {18688969},
year = {2020},
volume = {181},
editor = {Yixin Cao and SiuWing Cheng and Minming Li},
publisher = {Schloss DagstuhlLeibnizZentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/opus/volltexte/2020/13382},
URN = {urn:nbn:de:0030drops133820},
doi = {10.4230/LIPIcs.ISAAC.2020.38},
annote = {Keywords: 2connectivity, cut pairs, strongly connected components}
}
Keywords: 

2connectivity, cut pairs, strongly connected components 
Collection: 

31st International Symposium on Algorithms and Computation (ISAAC 2020) 
Issue Date: 

2020 
Date of publication: 

04.12.2020 