A Simple Test on 2-Vertex- and 2-Edge-Connectivity

TL;DR

This paper introduces a simpler linear-time algorithm for determining 2-vertex- and 2-edge-connectivity in graphs, efficiently identifying bridges and cut vertices with straightforward implementation.

Contribution

It presents a new, simpler linear-time algorithm that computes graph connectivity structures from which both 2-vertex- and 2-edge-connectivity can be easily derived.

Findings

Algorithm computes all bridges and cut vertices in linear time

Simplifies the process of testing 2-vertex- and 2-edge-connectivity

Provides an easier implementation compared to existing methods

Abstract

Testing a graph on 2-vertex- and 2-edge-connectivity are two fundamental algorithmic graph problems. For both problems, different linear-time algorithms with simple implementations are known. Here, an even simpler linear-time algorithm is presented that computes a structure from which both the 2-vertex- and 2-edge-connectivity of a graph can be easily "read off". The algorithm computes all bridges and cut vertices of the input graph in the same time.