We introduce two measures of imbalance, the team imbalance, and the field imbalance, in a tournament design. In addition to an exhaustive study of imbalances in tournament designs with up to eight teams, we present some bounds on the imbalances, as well as recursive constructions for homogeneous tournaments.

An arc in a tournament T with n 3 vertices is called k-pancyclic, if it belongs to a cycle of length for all k n. In this paper, we show that each s-strong tournament with s 3 contains at least s + 1 vertices whose out-arcs are 4-pancyclic. © 2006 Elsevier B.V. All rights reserved.

The maximum antichain cardinality (MACC) of a tournament is the maximum number of incomparable subtournaments of T . We establish some properties of MACC. We describe all tournaments whose MACC is 1 or 2, show that MACC can grow exponentially with the size of the vertex set of a tournament, and present some questions for further investigation.

Sumner’s universal tournament conjecture states that any tournament on 2n−2 vertices contains any directed tree on n vertices. In this paper we prove that this conjecture holds for all sufficiently large n. The proof makes extensive use of results and ideas from a recent paper by the same authors, in which an approximate version of the conjecture was

A tournament T,, consists of a set of n vertices and a single directed edge joining every pair of distinct vertices. We denote the vertices of T’. by {l, . . . , n). A permutation aI, . . . , a, of the vertices is a generalized path. The type af the path is characterized by the sequence a,_1 = e3 l l l E~__~ where si = i-1 if e -+ ai+1 and 6 = -1 if a, -+ ai tl. We also say that mn_l is realize...

Competitive high ranking positions are largely occupied by men, and women remain scarce in engineering and sciences. Explanations for these occupational differences focus on discrimination and preferences for work hours and field of study. We examine if absent these factors gender differences in occupations may still occur. Specifically we explore whether women and men, on a leveled playing fie...