Immersion of transitive tournaments in digraphs with large minimum outdegree

TL;DR

This paper proves that large minimum outdegree in a simple digraph guarantees the immersion of a transitive tournament of a given size, resolving a longstanding conjecture in graph theory.

Contribution

It establishes the existence of a function h(k) ensuring transitive tournament immersion in digraphs with sufficiently large outdegree, solving a notable conjecture.

Findings

Existence of a function h(k) for transitive tournament immersion

Digraphs with outdegree > h(k) contain the desired immersion

Resolution of a conjecture by Devos et al.

Abstract

We prove the existence of a function $h(k)$ such that every simple digraph with minimum outdegree greater than $h(k)$ contains an immersion of the transitive tournament on $k$ vertices. This solves a conjecture of Devos, McDonald, Mohar and Scheide.