For a tournament T , let ν3(T ) denote the maximum number of pairwise edge-disjoint triangles (directed cycles of length 3) in T . Let ν3(n) denote the minimum of ν3(T ) ranging over all regular tournaments with n vertices (n odd). We conjecture that ν3(n) = (1 + o(1))n /9 and prove that n 11.43 (1− o(1)) ≤ ν3(n) ≤ n 9 (1 + o(1)) improving upon the best known upper bound of n −1 8 and lower bou...

The Bermond-Thomassen conjecture states that, for any positive integer r, a digraph of minimum out-degree at least 2r−1 contains at least r vertex-disjoint directed cycles. Thomassen proved that it is true when r = 2, and very recently the conjecture was proved for the case where r = 3. It is still open for larger values of r, even when restricted to (regular) tournaments. In this paper, we pre...

This paper presents an experimental study of different variants of tournament selection, and proposes a new DISPAR-tournament (Disjoint Sets Parallel tournament) operator for population reduction to be used in parallel implementations of evolution strategies and other evolutionary algorithms.

Tournament selection is a useful and robust selection mechanism commonly used by genetic algorithms. The selection pressure of tournament selection directly varies with the tournament size | the more competitors , the higher the resulting selection pressure. This article develops a model, based on order statistics, that can be used to quantitatively predict the resulting selection pressure of a...

The idea that Operational Research can be used to optimise the design of a sporting contest or tournament is a novel one. This paper considers a methodology for this purpose. We propose a number of tournament metrics that can be used to measure the success of a sporting contest or tournament, and describe how these metrics may be evaluated for a particular tournament design. Knowledge of these ...

We consider the problem of using simulation to efficiently estimate the win probabilities for participants in a general random knockout tournament. Both of our proposed estimators, one based on the notion of “observed survivals” and the other based on conditional expectation and post-stratification, are highly effective in terms of variance reduction when compared to the raw simulation estimato...

Tournament solutions provide methods for selecting the best alternatives from a tournament and have found applications in a wide range of areas. Previous work has shown that several well-known tournament solutions almost never rule out any alternative in large random tournaments. Nevertheless, all analytical results thus far have assumed a rigid probabilistic model, in which either a tournament...

A single-elimination (SE) tournament is a popular way to select a winner in both sports competitions and in elections. A natural and well-studied question is the tournament fixing problem (TFP): given the set of all pairwise match outcomes, can a tournament organizer rig an SE tournament by adjusting the initial seeding so that their favorite player wins? We prove new sufficient conditions on t...

We propose a systematic methodology for defining tournament solutions as extensions of maximality. The central concepts of this methodology are maximal qualified subsets and minimal stable sets. We thus obtain an infinite hierarchy of tournament solutions, encompassing the top cycle, the uncovered set, the Banks set, the minimal covering set, and the tournament equilibrium set. Moreover, the hi...

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.