Edge Colourings of Graphs Avoiding Monochromatic Matchings of a Given Size

Let k and l be positive integers. With a graph G, we associate the quantity c(k,l)(G), the number of k-colourings of the edge set of G with no monochromatic matching of size l. Consider the function c(k,l) : N --> N given by c(k,l)(n) = max {c(k,l)(G): vertical bar V(G)vertical bar = n}, the maximum of c(k,l)(G) over all graphs G on n vertices. In this paper, we determine c(k,l)(n) and the corresponding extremal graphs for all large n and all fixed values of k and l.

Properly coloured copies and rainbow copies of large graphs with small maximum degree

Let G be a graph on n vertices with maximum degree ?. We use the Lovasz local lemma to show the following two results about colourings ? of the edges of the complete graph Kn. If for each vertex v of Kn the colouring ? assigns each colour to at most (n - 2)/(22.4?2) edges emanating from v, then there is a copy of G in Kn which is properly edge-coloured by ?. This improves on a result of Alon, Jiang, Miller, and Pritikin [Random Struct. Algorithms 23(4), 409433, 2003]. On the other hand, if ? assigns each colour to at most n/(51?2) edges of Kn, then there is a copy of G in Kn such that each edge of G receives a different colour from ?. This proves a conjecture of Frieze and Krivelevich [Electron. J. Comb. 15(1), R59, 2008]. Our proofs rely on a framework developed by Lu and Szekely [Electron. J. Comb. 14(1), R63, 2007] for applying the local lemma to random injections. In order to improve the constants in our results we use a version of the local lemma due to Bissacot, Fernandez, Procacci, and Scoppola [preprint, arXiv:0910.1824]. (c) 2011 Wiley Periodicals, Inc. Random Struct. Alg., 40, 425436, 2012

Characteristics of violence against children in a Brazilian Capital

The purpose of this exploratory, descriptive and retrospective study with a quantitative approach was to characterize violence against children in Curitiba. Reports of 2004 through 2008 about compulsory denouncements of violence cases were analyzed. The results showed an increase in violence, with home violence as the most frequent type and five to nine-year-olds as the most affected group, and negligence and physical violence as the most denounced forms of violence. Almost 81% of the sexual violence is performed against girls and the father is the main aggressor, showing inequality in gender relations and between generations. The importance of notification as a visibility instrument is highlighted. Other confrontation measures are necessary though, such as the promotion of equitable relationships of gender and generation, and cross-sectional policies that involve the social segments in a praxis that transforms reality.

Benchmarking sustainable urban mobility: The case of Curitiba, Brazil

Transportation planning is currently being confronted with a broader planning view, which is given by the concept of mobility. The Index of Sustainable Urban Mobility (I_SUM) is among the tools developed for supporting this new concept implementation. It is a tool to assess the current mobility conditions of any city, which can also be applied for policy formulation. This study focus on the application of I_SUM in the city of Curitiba, Brazil. Considering that the city is known worldwide as a reference of successful urban and transportation planning, the index application must confirm it. An additional objective of the study was to evaluate the index itself, or the subjacent assessment method and reference values. A global I_SUM value of 0.747 confirmed that the city has indeed very positive characteristics regarding sustainable mobility policies. However, some deficiencies were also detected, particularly with respect to non-motorized transport modes. The application has also served to show that a few I_SUM indicators were not able to capture some of the positive aspects of the city, what may suggest the need of changes in their formulation. Finally, the index application in parts of the city suggests that the city provides fair and equitable mobility conditions to all citizens throughout the city. This is certainly a good attribute for becoming a benchmark of sustainable mobility, even if it is not yet the ideal model. (C) 2012 Elsevier Ltd. All rights reserved.

Resíduos sólidos urbanos: impactos socioambientais e perspectiva de manejo sustentável com inclusão social

Com a Rio+20 retoma-se a discussão de estratégias para conciliar desenvolvimento com proteção dos ecossistemas. Um tema apenas tangenciado nessas discussões é o gerenciamento dos resíduos sólidos urbanos. Diante da institucionalização da Política Nacional de Resíduos Sólidos, busca-se contribuir para esse debate, bem como apontar caminhos para o enfrentamento dessa questão, privilegiando a inclusão social. Para isso, foram utilizados documentos e informações sobre a gestão de resíduos sólidos, e a literatura científica especializada. Observa-se que o inadequado gerenciamento dos resíduos sólidos gera impactos imediatos no ambiente e na saúde, assim como contribui para mudanças climáticas. Considerando as limitações das opções de destinação final para os resíduos, é imprescindível minimizar as quantidades produzidas por meio da redução, reutilização e reciclagem. Nesse contexto, destaca-se o papel dos catadores, que vêm realizando um trabalho de grande importância ambiental. Dadas as fragilidades desse segmento populacional, é preciso delinear políticas públicas que tornem a atividade de catação mais digna e com menos riscos e que, ao mesmo tempo, garantam renda, para assim caminhar rumo a um desenvolvimento mais saudável, justo e sustentável.