We study combinatorial and algorithmic questions around minimal feedback vertex sets in tournament graphs. On the combinatorial side, we derive strong upper and lower bounds on the maximum number of minimal feedback vertex sets in an n-vertex tournament. We prove that every tournament on n vertices has at most 1.6740 minimal feedback vertex sets and that there is an infinite family of tournamen...

It is well known that every tournament contains a Hamiltonian path, which can be restated as that every tournament contains a unary spanning tree. The purpose of this article is to study the general problem of whether a tournament contains a k-ary spanning tree. In particular, we prove that, for any fixed positive integer k, there exists a minimum number h(k) such that every tournament of order...

The standard tournament selection samples individuals with replacement. The sampling-with-replacement strategy has its advantages but also has issues. One of the commonly recognised issues is that it is possible to have some individuals not sampled at all during the selection phase. The not-sampled issue aggravates the loss of diversity. However, it is not clear how the issue affects GP search....

This note uncovers new properties of the von Neumann-Morgenstern solution in weak tournaments and majoritarian games. We propose a new procedure for the construction of choice sets from weak tournaments, based on dynamic stability criteria. The idea is to analyze dynamic versions of the tournament game introduced by Laffond, Laslier and Le Breton (1993) [The bipartisan set of a tournament game....

Consider the following problem in game manipulation. A tournament designer who has full knowledge of the match outcomes between any possible pair of players would like to create a bracket for a balanced single-elimination tournament so that their favorite player will win. Although this problem has been studied in the areas of voting and tournament manipulation, it is still unknown whether it ca...

In this paper, we improve the best-known upper bound on the size of maximal tournament codes, and solve the related problem of edge-covering a complete graph with a minimum number of bipartite graphs of bounded size. Tournament codes are sets of {0,1,∗} strings closely related to self-synchronizing codes. We improve the current asymptotic upper bound on the size of a length-k tournament code (g...

Given a tournament score sequence s1 s2 } } } sn , we prove that there exists a tournament T on vertex set [1, 2, ..., n] such that the degree of any vertex i is si and the subtournaments of T on both the even and the odd vertices are transitive in the given order. This means that i beats j whenever i< j and i# j (mod 2). For any score sequence, we give an algorithm to construct a tournament of...

The (0, 1)-matrix A of order n is a tournament matrix provided A + A + I = J, where I is the identity matrix, and J = Jn is the all 1’s matrix of order n. It was shown by de Caen and Michael that the rank of a tournament matrix A of order n over a field of characteristic p satisfies rankp(A) ≥ (n − 1)/2 with equality if and only if n is odd and AA = O. This article shows that the rank of a tour...

A fundamental property of choice functions is stability, which, loosely speaking, prescribes that choice sets are invariant under adding and removing unchosen alternatives. We provide several structural insights that improve our understanding of stable choice functions. In particular, (i) we show that every stable choice function is generated by a unique simple choice function, which never excl...

We argue that financial analysts can be viewed as participants of two tournaments (the “All-star” tournament and the intrafirm tournament) and examine whether analysts are incentivized by the tournament compensation structure. Using data from 1991 to 2007, we find that interim losers are more likely to increase the boldness of their forecasts in the remainder of the tournament period than inter...