Compositions of Digraphs: A Survey

TL;DR

This survey reviews known results and presents new findings on digraph compositions, covering topics like connectivity, kernels, paths, cycles, and spanning subdigraphs, while highlighting open problems in the field.

Contribution

It provides a comprehensive overview of digraph compositions, introduces new results, and discusses conjectures and open problems in the area.

Findings

New results on digraph compositions and their properties.

Identification of open problems and conjectures for future research.

Enhanced understanding of connectivity, kernels, and spanning subdigraphs in digraph compositions.

Abstract

In this survey we overview known results and get several new results on digraph compositions which generalize several classes of digraphs, such as quasi-transitive digraphs. After an introductory section, the paper is divided into six sections: connectivity and linkages, kings and kernels, paths, cycles, acyclic spanning subdigraphs, strong spanning subdigraphs. This survey also contains some conjectures and open problems for further study.