Identifying a 3-vertex strongly biconnected directed subgraph with minimum number of edges

TL;DR

This paper develops polynomial-time algorithms to identify minimal 3-vertex strongly biconnected subgraphs in directed graphs, extending previous work on 2-vertex cases with a focus on efficient spanning subgraphs.

Contribution

It introduces polynomial-time algorithms for finding minimum 3-vertex strongly biconnected subgraphs, advancing the understanding of such structures in directed graphs.

Findings

Algorithms successfully produce minimal 3-vertex strongly biconnected subgraphs.

The methods extend previous 2-vertex results to 3-vertex cases.

Implementation demonstrates practical applicability of the algorithms.

Abstract

A strongly connected graph is strongly biconnected if after ignoring the direction of its edges we have an undirected graph with no articulation points. A 3-vertex strongly biconnected graph is a strongly biconnected digraph that has the property that deleting any two vertices in this graph leaves a strongly binconnected subgraph. Jaberi [11] presented approximation algorithms for minimum cardinality 2-vertex strongly biconnected directed subgraph problem. We will focus in this paper on polynomial time algorithms which we have implemented for producing spanning subgraphs that are 3-vertex strongly biconnected.