A tournament is unimodular if the determinant of its skew-adjacency matrix $1$. In this paper, we give some properties and constructions tournaments. $T$ with $S$ invertible $S^{-1}$ a tournament. spectral characterization tournaments given. Lastly, show that every $n$-tournament can be embedded in by adding at most $n - \lfloor\log_2(n)\rfloor$ vertices.

The development of men's handball was analyzed using data from the Olympic, World and European Championships held within the last eight years. The most obvious change, especially within these last nine tournaments, was that men's handball was played more dynamically and rapidly, both in attack and defense, especially by European teams. The first aim of this study was to conduct a technical anal...

In this thesis we shall deal with oriented graphs. The motivation for us is a result by Sali and Simonyi (see also a short proof by Gyárfás) where the existence of the decomposition of transitive tournaments on two isomorphic graphs is shown. In this thesis we start to study a problem of packing in transitive tournaments and we consider decompositions and partitions of transitive tournaments. T...

In sport tournaments where teams compete in match play format, the pairing of players in matches is critical to the final outcomes. This paper presents simulation models using only commonplace spreadsheet software to analyze and compare strategies in such pairings based on actual or estimated performance of individual players. The approach can be a useful decision support tool for captains and ...

We introduces the umodules, a generalisation of the notion of graph module. The theory we develop captures among others undirected graphs, tournaments, digraphs, and 2−structures. We show that, under some axioms, a unique decomposition tree exists for umodules. Polynomial-time algorithms are provided for: non-trivial umodule test, maximal umodule computation, and decomposition tree computation ...

A king in a directed graph is a node from which each node in the graph can be reached via paths of length at most two. There is a broad literature on tournaments (completely oriented digraphs), and it has been known for more than half a century that all tournaments have at least one king [Lan53]. Recently, kings have proven useful in theoretical computer science, in particular in the study of t...

Tournaments are without doubt the best studied class of directed graphs [3, 6]. The generalizations of tournaments arise in order to extend the well-known results on tournaments to more general classes of directed graphs. Moreover, the knowledge about generalizations of tournaments has allowed to deepen our understanding of tournaments themselves. The semicomplete digraphs, the semicomplete mul...