Partitioning a tournament into sub-tournaments of high connectivity

TL;DR

This paper proves that strongly connected tournaments can be partitioned into sub-tournaments with high connectivity, confirming a conjecture and establishing tight bounds up to a constant factor.

Contribution

It establishes a partitioning theorem for strongly connected tournaments, confirming a conjecture and providing tight bounds up to a constant factor.

Findings

Existence of a constant c for partitioning strongly c·kt-connected tournaments into t strongly k-connected sub-tournaments.

The result is tight up to a constant factor.

Confirms a conjecture by K"uhn, Osthus, and Townsend (2016).

Abstract

We prove that there exists a constant $c > 0$ such that the vertices of every strongly $c \cdot kt$-connected tournament can be partitioned into $t$ parts, each of which induces a strongly $k$-connected tournament. This is clearly tight up to a constant factor, and it confirms a conjecture of K\"uhn, Osthus and Townsend (2016).