Immersion of complete digraphs in Eulerian digraphs

Abstract

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 P uv , for uv ∈ E ( H ), such that P uv 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.