# Transitive tournament tilings in oriented graphs with large minimum total degree

## TL;DR

This paper proves that large oriented graphs with high minimum total degree can be partitioned into transitive tournaments, specifically $oldsymbol{ ext{T}_4}$, and improves bounds for such partitions in general.

## Contribution

It establishes asymptotically tight bounds for partitioning oriented graphs into transitive tournaments, advancing understanding of graph tilings with high minimum total degree.

## Key findings

- Partitioning into T4 is possible with degree $(11/12+o(1))n$
- Bound is asymptotically tight for T4
- Improves bounds for general T_k partitions

## Abstract

Let $\vec{T}_k$ be the transitive tournament on $k$ vertices. We show that every oriented graph on $n=4m$ vertices with minimum total degree $(11/12+o(1))n$ can be partitioned into vertex disjoint $\vec{T}_4$'s, and this bound is asymptotically tight. We also improve the best known bound on the minimum total degree for partitioning oriented graphs into vertex disjoint $\vec{T}_k$'s.