On the Graceful Game

A graceful labeling of a graph $G$ with $m$ edges consists of labeling the vertices of $G$ with distinct integers from $0$ to $m$ such that, when each edge is assigned as induced label the absolute difference of the labels of its endpoints, all induced edge labels are distinct. Rosa established two well known conjectures: all trees are graceful (1966) and all triangular cacti are graceful (1988). In order to contribute to both conjectures we study graceful labelings in the context of graph games. The Graceful game was introduced by Tuza in 2017 as a two-players game on a connected graph in which the players Alice and Bob take turns labeling the vertices with distinct integers from 0 to $m$. Alice's goal is to gracefully label the graph as Bob's goal is to prevent it from happening. In this work, we study winning strategies for Alice and Bob in complete graphs, paths, cycles, complete bipartite graphs, caterpillars, prisms, wheels, helms, webs, gear graphs, hypercubes and some powers of paths

Graceful game on some graph classes

A graceful labeling of a graph $G$ with $m$ edges consists in labeling the vertices of $G$ with distinct integers from $0$ to $m$ such that each edge is uniquely identified by the absolute difference of the labels of its endpoints. In this work, we study the graceful labeling problem in the context of maker-breaker graph games. The Graceful Game was introduced by Tuza, in 2017, as a two-players game on a connected graph in which the players, Alice and Bob, take moves labeling the vertices with distinct integers from $0$ to $m$. Players are constrained to use only legal labelings (moves), that is, after a move, all edge labels are distinct. Alice's goal is to obtain a graceful labeling for the graph, as Bob's goal is to prevent it from happening. In this work, we study winning strategies for Alice and Bob in graph classes: paths, complete graphs, cycles, complete bipartite graphs, caterpillars, trees, gear graphs, web graphs, prisms, hypercubes,  2-powers of paths, wheels and fan graphs

Brasil-Estados Unidos: desafios de um relacionamento assimétrico

O artigo analisa alguns dos desafios com que o Brasil se depara no relacionamento com os Estados Unidos desde o final da Segunda Guerra Mundial. Durante a Guerra Fria, o Brasil tendeu a se alinhar ideologicamente aos Estados Unidos enquanto buscava o desenvolvimento. Com o fim da Guerra Fria percebe-se a adoção de uma política desnacionalizante e de defesa de interesses tópicos nas divergências com os Estados Unidos. No século XXI, o desafio será a integração econômica. Nesse contexto, a ALCA, caso se concretize, trará a necessidade de administrar uma divergência estratégica entre os dois países.<br>The article analyses some of the challenges Brazil has faced in its relationship with the United States since the end of the Second World War. During the Cold War, Brazil struggled to develop while it tended to be ideologically aligned to the United States. After the end of the Cold War, Brazil pursued denationalization policies and defended some minor interests against the United States. Economic integration is the challenge on the 21th century. In this context, the FTAA - Free Trade Area of Americas - will make it necessary for this two countries to administrate strategic differences, if it comes to reality

Reforma do estado: o privado contra o público The reform of the state: the private versus the public

A reforma do Estado está situada no centro da agenda dos países periféricos, obedece às condicionalidades do Fundo Monetário Internacional (FMI) e do Banco Mundial, assim como está presente nas políticas que ampliam a esfera privada em detrimento da pública. O determinismo tecnológico - expresso por meio da ideologia da globalização - e o uso de um léxico em que o discurso da direita e da esquerda parecem se confundir - como nos temas da autonomia, da sociedade civil e da crítica ao estatismo - contribuem para a formação da ideologia dominante. Critica-se, aqui, o discurso que confere inexorabilidade a essas reformas, sustenta a ruptura com a política macroeconômica neoliberal para que a transição pós-neoliberal possa ser concretizada e defende a oposição entre o público e o privado como estratégica para a construção de alternativas. Argumenta-se que as reformas aprofundam a condição capitalista dependente do país e ampliam a sua heteronomia cultural, agravando o apartheid educacional e científico-tecnológico, com graves conseqüências sociais. Discute-se, ainda, que a construção de um Estado ético, p��blico, requer o fortalecimento dos movimentos sociais, a autonomia vis-à-vis aos governos e a elaboração de teorias críticas em relação ao Estado, em uma sociedade não subjugada à ordem do capital.<br>The reform of the State is at the centre of the periphery countries' agenda; it fulfils the conditions imposed by the International Monetary Fund and by the World Bank, as well as being part of the policies that aim at expanding the private sphere in detriment of the public one. Technological determinism - expressed by the globalisation ideology - and the use of a vocabulary that makes the discourses of both left and right seem very similar (as it occurs in the case of matters such as autonomy, civil society and the critique of statism) contribute towards the construction of the dominant ideology. Here we make a critique of the discourse that makes these reforms seem inexorable, support the rupture with the neo-liberal macroeconomic policies in order to guarantee the concretisation of the post neo-liberal transition and defend the opposition between the public and the private as a strategy for the construction of alternatives. We argue that the reforms will strengthen the dependent capitalist condition of this country and, widening its cultural heteronomy, will further intensify the existing educational and technological-scientific apartheid, with serious social consequences. We also suggest that the construction of an ethical and public State demands the strengthening of social movements, their autonomy vis-à-vis governments and the elaboration of critical theories related to the State in a society that is not subdued to the order of Capital

Contribuições da Sociologia na América Latina à imaginação sociológica: análise, crítica e compromisso social Sociology's contribution in Latin America to sociological imagination: analysis, critique, and social commitment

O artigo aborda o papel desempenhado pela Sociologia na análise dos processos de transformação das sociedades latino-americanas, no acompanhamento do processo de construção do Estado e da Nação, na problematização das questões sociais na América Latina. São analisados seis períodos na Sociologia na América Latina e no Caribe: I) a herança intelectual da Sociologia ; II) a sociologia da cátedra; III) O período da "Sociologia Científica" e a configuração da "Sociologia Crítica"; IV) a crise institucional, a consolidação da "Sociologia Crítica" e a diversificação da sociologia; V) a sociologia do autoritarismo, da democracia e da exclusão; VI) a consolidação institucional e a mundialização da sociologia da América Latina (desde o ano de 2000), podendo-se afirmar que os traços distintivos do saber sociológico no continente foram: o internacionalismo, o hibridismo, a abordagem crítica dos processos e conflitos das sociedades latino-americanas e o compromisso social do sociólogo.<br>The article focuses on the role played by Sociology in the analysis of processes of change in Latin American societies, in the process of construction of Nation and State, in the debate of social issues in Latin America and the Caribbean. Six periods in Sociology in Latin America and the Caribbean are examined: I) sociology's intellectual legacy; II) sociology as a cathedra; III) the period of "Scientific Sociology"; IV) the institutional crisis, the consolidation of "Critical Sociology", and the diversifying of sociology; V) sociology of authoritarianism, democracy and exclusion; VI) institutional consolidation and globalization of Latin American sociology (since 2000). It may be said that the distinctive features of sociological knowledge in the continent were: internationalism, hybridism, the critical approach to processes and conflicts of Latin American societies, and the sociologist social commitment