We study a high-dimensional analog for the notion of an acyclic (aka transitive) tournament. We give upper and lower bounds on the number of d-dimensional n-vertex acyclic tournaments. In addition, we prove that every n-vertex d-dimensional tournament contains an acyclic subtournament of (log1/d n) vertices and the bound is tight. This statement for tournaments (i.e., the case d = 1) is a well-...

A k-majority tournament is realized by 2k−1 linear orders on the set of vertices, where a vertex u dominates v if u precedes v in at least k of the orders. Various properties of such tournaments have been studied, among them the problem of finding the size of a smallest dominating set. It is known that 2-majority tournaments are dominated by 3 vertices and that k-majority tournaments are domina...

Complementing recent progress on classical complexity and polynomial-time approximability of feedback set problems in (bipartite) tournaments, we extend and partially improve fixed-parameter tractability results for these problems. We show that Feedback Vertex Set in tournaments is amenable to the novel iterative compression technique. Moreover, we provide data reductions and problem kernels fo...

Astit-Vidal, A. and V. Dugat, Autonomous parts and decomposition of regular tournaments, Discrete Mathematics 111 (1993) 27-36. In this article we present the action of a decomposition criterion for regular tournaments, called W-decomposition on tournaments presenting autonomous parts, and especially those that are undecomposable with respect to W-decomposition.

Rank-order tournaments are usually modeled simultaneously. However, real tournaments are often sequential. We show that agents’ strategic behavior in sequential-move tournaments significantly differ from the one in simultaneous-move tournaments: In a sequential-move tournament with heterogeneous agents, there may be either a first-mover or a second-mover advantage. Under certain conditions the ...

Professional tennis organizations, such as the United States Tennis Association (USTA), the Association of Tennis Professionals (ATP), the International Tennis Federation (ITF), and the Women’s Tennis Association (WTA), host tennis tournaments throughout the world. At these tournaments, chief umpires assign and schedule line umpires for every match. For most tournaments, they perform this task ...

We study two-path convexity in bipartite tournaments. For a bipartite tournament, we obtain both a necessary condition and a sufficient condition on the adjacency matrix for its rank to be two. We then investigate 4-cycles in bipartite tournaments of small rank. We show that every vertex in a bipartite tournament of rank two lies on a four cycle, and bipartite tournaments with a maximum number ...

Crowdsourcing gains momentum: In digital work places such as Amazon Mechanical Turk, oDesk, Clickworker, 99designs, or InnoCentive it is easy to distribute human work to hundreds or thousands of freelancers. In these crowdsourcing settings, one challenge is to properly incent worker effort to create value. Common incentive schemes are piece rate payments and rankorder tournaments among workers....

Tournament embedding is an order relation on the class of finite tournaments. An antichain is a set of finite tournaments that are pairwise incomparable in this ordering. We say an antichain A can be extended to an antichain B if A ⊆ B. Those finite antichains that can not be extended to antichains of arbitrarily large finite cardinality are exactly those that contain a member of each of four f...

The present paper surveys the history of algebraic represetations of complete directed graphs, known in graph theory as tournaments, or equivalently, relational structures with a trichotomous binary relation. Essentially, two kinds of algebraizations of tournaments were studied in the literature: algebras with one binary operation (called groupoids of tournaments) and algebras with two binary o...