Menger's theorem for ends of digraphs

TL;DR

This paper extends Menger's theorem to ends of directed graphs, providing a new theoretical framework and characterizing the combined degree of these ends.

Contribution

The paper generalizes Menger's theorem to ends of digraphs, offering a novel theoretical extension in graph theory.

Findings

Extended Menger's theorem to ends of digraphs

Characterized the combined degree of ends of digraphs

Provided a new theoretical framework for directed graph ends

Abstract

Polat generalised Menger's theorem -- the maximum number of vertex-disjoint paths between two sets $A$ and $B$ equals the minimum size of an $A$-$B$ separator -- to ends of undirected graphs. In this paper we extend Menger's theorem to ends of digraphs. As an application, we characterise the combined degree of ends of digraphs.