Steiner Type Packing Problems in Digraphs: A Survey

TL;DR

This survey reviews known results and open problems related to directed Steiner type packing problems in digraphs, extending classical graph packing concepts to directed graphs.

Contribution

It provides a comprehensive overview of various directed Steiner packing problems, including conjectures and open questions, highlighting recent advances and future research directions.

Findings

Overview of directed Steiner tree packing problem

Discussion of directed Steiner path and pendant Steiner tree packing problems

Identification of open problems and conjectures in the field

Abstract

Graph packing problem is one of the central problems in graph theory and combinatorial optimization. The famous Steiner tree packing problem in undirected graphs has become an well-established area. It is natural to extend this problem to digraphs, and such problems in digraphs are called directed Steiner type packing problems. In this survey we overview known results on several directed Steiner type packing problems. The paper is divided into seven sections: introduction, directed Steiner tree packing problem, directed Steiner path packing problem, directed pendant Steiner tree packing problem, strong subgraph packing problem, strong arc decomposition problem, directed Steiner cycle packing problem. This survey also contains some conjectures and open problems for further study.