Acyclicity in edge-colored graphs

A walk $W$ in edge-colored graphs is called properly colored (PC) if every pair of consecutive edges in $W$ is of different color. We introduce and study five types of PC acyclicity in edge-colored graphs such that graphs of PC acyclicity of type $i$ is a proper superset of graphs of acyclicity of type $i+1$, $i=1,2,3,4.$ The first three types are equivalent to the absence of PC cycles, PC trails, and PC walks, respectively. While graphs of types 1, 2 and 3 can be recognized in polynomial time, the problem of recognizing graphs of type 4 is, somewhat surprisingly, NP-hard even for 2-edge-colored graphs (i.e., when only two colors are used). The same problem with respect to type 5 is polynomial-time solvable for all edge-colored graphs. Using the five types, we investigate the border between intractability and tractability for the problems of finding the maximum number of internally vertex disjoint PC paths between two vertices and the minimum number of vertices to meet all PC paths between two vertices

On Graphs with Proper Connection Number 2

An edge-colored graph is properly connected if for every pair of vertices u and v there exists a properly colored uv-path (i.e. a uv-path in which no two consecutive edges have the same color). The proper connection number of a connected graph G, denoted pc(G), is the smallest number of colors needed to color the edges of G such that the resulting colored graph is properly connected. An edge-colored graph is flexibly connected if for every pair of vertices u and v there exist two properly colored paths between them, say P and Q, such that the first edges of P and Q have different colors and the last edges of P and Q have different colors. The flexible connection number of a connected graph G, denoted fpc(G), is the smallest number of colors needed to color the edges of G such that the resulting colored graph is flexibly connected. In this paper, we demonstrate several methods for constructing graphs with pc(G) = 2 and fpc(G) = 2. We describe several families of graphs such that pc(G) ≥ 2 and we settle a conjecture from [BFG+12]. We prove that if G is connected and bipartite, then pc(G) = 2 is equivalent to being 2-edge-connected and fpc(G) = 2 is equivalent to the existence of a path through all cut-edges. Finally, it is proved that every connected, k-regular, Class 1 graph has flexible connection number 2

The construction of a unit and workbook of exercises for the slow learner to develop comprehension and increase study skills for use in the teaching of an American history unit on the westward movement in the United States on a sixth grade level.

Thesis (Ed.M.)--Boston University N.B.:pages missing: 170, 171, 173 from original cop

Promoting Bicycle Commuter Safety, Research Report 11-08

We present an overview of the risks associated with cycling to emphasize the need for safety. We focus on the application of frameworks from social psychology to education, one of the 5 Es—engineering, education, enforcement, encouragement, and evaluation. We use the structure of the 5 Es to organize information with particular attention to engineering and education in the literature review. Engineering is essential because the infrastructure is vital to protecting cyclists. Education is emphasized since the central focus of the report is safety

From extraction to commercialization: an analysis of the timber supply chain in the brazilian legal amazon

The production chain of the Brazilian forestry sector plays a crucial role in the global economy, providing a wide variety of products used in construction and industrial processes. The extraction of timber from native forests is essential for the production of paper, furniture, and charcoal, driving the economy through exports. However, the expansion of this sector faces challenges related to the lack of environmental conservation policies, infrastructure, financing, and the pressure of illegal deforestation. This article aims to enhance the description of the timber production process in the Brazilian Legal Amazon region, addressing its stages, procedures, and necessary considerations for sustainable extraction in accordance with environmental laws. A case study was conducted in a timber company in Porto Acre, Acre, involving literature review and a questionnaire administered to the responsible manager. The timber extraction process requires document analysis, legal compliance, and field surveys. Projects are developed to determine which tree species can be harvested, with a priority given to young trees and those with seeds, as well as considering protected areas. After project approval, camps and roads are set up to initiate the exploitation. The logistics involve the construction and maintenance of roads, temporary bridges, and storage yards, utilizing heavy machinery to clear paths, drag logs, and load trucks. The careful placement of storage yards considers biodiversity and ecosystem protection. Through a continuous commitment to responsible forest management, it is possible to reconcile economic activity with nature conservation, ensuring a sustainable future for native forests.A cadeia produtiva do setor florestal brasileiro desempenha um papel fundamental na economia global, fornecendo uma ampla variedade de produtos utilizados na construção civil e processos industriais. A extração de madeira em florestas nativas é um processo essencial para a produção de papel, móveis e carvão, impulsionando a economia por meio da exportação. No entanto, a expansão desse setor enfrenta desafios relacionados à falta de políticas de conservação ambiental, infraestrutura, financiamento e pressão do desmatamento ilegal. Este artigo tem como objetivo aprimorar a descrição do processo de produção da madeira na região da Amazônia Legal brasileira, abordando suas etapas, procedimentos e considerações necessárias para uma extração sustentável em conformidade com as leis ambientais. Um estudo de caso foi realizado em uma empresa madeireira no município de Porto Acre, Acre, envolvendo revisão da literatura e aplicação de um questionário ao gerente responsável. O processo de extração de madeira requer análise documental, conformidade legal e levantamento de campo. Projetos são elaborados para determinar quais espécies de árvores podem ser cortadas, priorizando as jovens e as que têm sementes, além das áreas de proteção. Após a aprovação dos projetos, acampamentos e estradas são montados para iniciar a exploração. A logística envolve a construção e manutenção de estradas, pontes temporárias e pátios de armazenamento, com o uso de máquinas pesadas para abrir caminhos, arrastar toras e carregar caminhões. A localização cuidadosa dos pátios de armazenamento leva em consideração a biodiversidade e a proteção do ecossistema. Por meio de um compromisso contínuo com o manejo florestal responsável, é possível conciliar a atividade econômica com a conservação da natureza, assegurando um futuro sustentável para as florestas nativas

Under the bridges of Warsaw: transformation of unused spaces located under the viaducts of bridges in Warsaw, Poland

The research concerns various aspects of the impact of megastructures on shaping the city, their role in creating urban envrionment, as well as the transition from the large-scale to the human scale.Due to the increased phenomenon of urban development and the decreasing number of available spaces in the city, the work tries to find a way to use neglected non-obvious spaces in the city.The work focuses on the revitalization of unused spaces located under the viaducts of the Poniatowski Bridge,Łazienkowski Bridge and Świętokrzyski Bridge in Warsaw,Poland.In the context of analyzing the potential of space under viaducts in Warsaw,the work examines the impact of megastructures on the city in the visual and social context.Cultural, social and spatial aspects related to the existence of large-scale objects such as bridges are studied. An important point of analysis is the use of the potential of neglected spaces under the bridges. The work focuses on identifying these areas as a source of spatial opportunities that can contribute to the removal of discontinuities in the city.Research look for a different ways to transform these spaces into public spaces that meet the needs of local communities. Work discusses the concept of the potential of unused land and the phenomenon of social closure among young citizens in Warsaw.The ways in which color and art can influence the perception of the space under viaducts are also being explored.The work also focuses on understanding how the Vistula River and the history of the city affect the current state of space and the quality of life of Warsaw residents.The reference to the river and the history of the city aims to capture the context in which the unused spaces under the viaducts are located, and to identify ways in which they can be transformed,taking into account the unique features of Warsaw.Research is supported by the analysis of theoretical issues and similar cases in the field of architecture, photography,literature and art