# Decomposition of balanced multipartite tournaments into strongly connected tournaments

## TL;DR

This paper investigates conditions under which multipartite tournaments can be partitioned into strongly connected subtournaments, extending previous research on the structure and decomposition of directed graphs.

## Contribution

It advances the understanding of how multipartite tournaments can be decomposed into strongly connected components, building on prior work from 1999.

## Key findings

- Established conditions for the existence of such decompositions
- Extended previous results on strongly connected subtournaments
- Provided new insights into the structure of multipartite tournaments

## Abstract

Decomposing a digraph into subdigraphs with a fixed structure or property is a classical problem in graph theory and a useful tool in a number of applications of networks and communication. A digraph is strongly connected if it contains a directed path from each vertex to all others. In this paper we consider multipartite tournaments, and we study the existence of a partition of a multipartite tournament with $c$ partite sets into strongly connected $c$-tournaments. This is a continuation of the study started in 1999 by Volkmann of the existence of strongly connected subtournaments in multipartite tournaments.