Immersion of complete digraphs in Eulerian digraphs

Abstract

A digraph G immerses a digraph H if there is an injection f: V(H) → V(G) and a collection of pairwise edge-disjoint directed paths Puv, for uv ∈ E(H), such that Puv starts at f(u) and ends at f(v). We prove that every Eulerian digraph with minimum out-degree t immerses a complete digraph on Ω(t) vertices, thus answering a question of DeVos, McDonald, Mohar and Scheide.