$2$-edge-twinless blocks

TL;DR

This paper introduces the concept of 2-edge-twinless blocks in directed graphs, characterizes their properties, and develops algorithms to efficiently compute these blocks, enhancing understanding of graph connectivity under edge removal.

Contribution

The paper defines 2-edge-twinless blocks in directed graphs and provides algorithms for their computation, advancing the analysis of twinless connectivity.

Findings

Defined 2-edge-twinless blocks in directed graphs

Developed algorithms for computing these blocks

Enhanced understanding of twinless connectivity under edge removal

Abstract

Let $G=(V,E)$ be a directed graph. A $2$-edge-twinless block in $G$ is a maximal vertex set $C^{t}\subseteq V$ with $|C^{t}|>1$ such that for any distinct vertices $v,w \in C^{t}$, and for every edge $e\in E$, the vertices $v,w$ are in the same twinless strongly connected component of $G\setminus\left \lbrace e \right\rbrace $. In this paper we study this concept and describe algorithms for computing $2$-edge-twinless blocks.