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 reform of Welfare Regimes in Costa Rica, Chile, Argentina, Brazil and Uruguay

The aim of this article is to analyze the social policy in Latin America in a context of emerging welfare states. To understand the changes one takes into consideration the theories about institutional reform and the transformations produced in the XX century and the beginning of the XXI to substitute a social security regime mainly based on segmentation of benefi ts and on programs to fi ght poverty by another with an institutional and redistributive nature. The paper pays attention in particular to the path of the most developed welfare states of Latin America: Costa Rica, Chile, Argentina, Brasil y Uruguay.

A delphy study of the cooperativisation of the social services in the historical territory of Gipuzkoa

This article shows the main results obtained from the Delphi study, which was made of politicians and technicians from the Department of Social Policy in the County Council of Gipuzkoa, concerning the possibility of cooperativizing the provision of social services in this historical territory. With this in mind, the structure of this article is in two different parts. The first part develops the theoretical framework which serves as inspiration for the empirical work, where note is made of the main theoretical proposals that have a bearing on the collective dimension of citizen participation in the management of public services. Among the various models, those which prioritise public participation through social and solidarity economy entities stand out. The second part concerns itself with the presentation of the field research results. To this end, the methodological notes concerning the preparation process for the Delphi analysis are presented first and this is immediately followed by a synthesis of the main results obtained in this study. The article ends with a section of conclusions and future lines of action.