Strong Subgraph Connectivity of Digraphs: A Survey

TL;DR

This survey reviews existing research on strong subgraph connectivity in directed graphs, covering fundamental results, algorithms, bounds, and open problems in the field.

Contribution

It compiles and discusses known results, conjectures, and open problems related to strong subgraph connectivity in digraphs, providing a comprehensive overview.

Findings

Summarizes key results on strong subgraph k-connectivity.

Identifies bounds and complexity results for related problems.

Highlights open problems and conjectures for future research.

Abstract

In this survey we overview known results on the strong subgraph $k$-connectivity and strong subgraph $k$-arc-connectivity of digraphs. After an introductory section, the paper is divided into four sections: basic results, algorithms and complexity, sharp bounds for strong subgraph $k$-(arc-)connectivity, minimally strong subgraph $(k, \ell)$-(arc-) connected digraphs. This survey contains several conjectures and open problems for further study.