Hall conditions for edge-weighted bipartite graphs

A weighted variant of Hall's condition for the existence of matchings is shown to be equivalent to the existence of a matching in a lexicographic product. This is used to introduce characterizations of those bipartite graphs whose edges may be replicated so as to yield semiregular multigraphs or, equivalently, semiregular edge-weightings. Such bipartite graphs will be called semiregularizable. Some infinite families of semiregularizable trees are described and all semiregularizable trees on at most 11 vertices are listed. Matrix analogues of some of the results are mentioned and are shown to imply some of the known characterizations of regularizable graphs.

The Influence of the Family in the Development of Talent in Sport

The purpose of the present study was to describe patterns in the dynamics of families of talented athletes throughout their development in sport. Four families, including three families of elite rowers and one family of an elite tennis player were examined. The framework provided by Ericsson, Krampe, and Tesch- Römer (1993) to explain expert performance served as the theoretical basis for the study. Ericsson et al. suggested that the acquisition of expert performance involves operating within three types of constraints: motivational, effort, and resource. In-depth interviews were conducted with each athlete, parent, and sibling to explore how they have dealt with these three constraints. A total of 15 individual interviews were conducted. Results permitted the identification of three phases of participation from early childhood to late adolescence: the sampling years, the specializing years, and the investment years. The dynamics of the family in each of these phases of development is discussed