Menger's theorem for ends of digraphs

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.