Biclique aresta-coloração por listas

Orientador : Prof. Dr. André Luiz Pires GuedesCoorientadora : Profª. Drª. Marina GroshausDissertação (mestrado) - Universidade Federal do Paraná, Setor de Ciências Exatas, Programa de Pós-Graduação em Informática. Defesa: Curitiba, 05/06/2017Inclui referências : f. 41-42Resumo: Na coloração de grafos existem algumas versões dos problemas de coloração de vértices e de coloração de arestas. Eles podem ser definidos a partir de conceitos como coloração por listas (colorir os elementos do grafo dados subconjuntos do conjunto de cores) ou colorir os elementos do grafo de forma que não existe uma estrutura monocromática. Um grafo G _e dito k-biclique aresta-selecionável se para qualquer atribuição de listas de cores para as arestas, onde cada lista tem tamanho k, existe uma coloração de E(G), onde cada aresta só pode usar as cores de sua lista, tal que não existe uma biclique (subgrafo induzido bipartido completo maximal) monocromática. Se k é o menor valor tal que G é k-biclique aresta-selecionável então k é o biclique índice de seleção de G. Assim nós podemos definir o k-biclique aresta-selecionabilidade como o problema de decidir se um grafo é k-biclique aresta-selecionável ou não. Nessa dissertação estudamos esse problema por provar que os grafos sem triangulo não isomorfo a um ciclo ímpar são 2-estrela aresta-selecionáveis (estrelas não monocromáticas), os bipartidos cordais são 2-biclique aresta-selecionáveis e mostramos um limite inferior do biclique índice de seleção dos grafos potencias de ciclos e potências de caminhos. E também apresentamos algoritmos polinomiais para computar uma 2-biclique (estrela) aresta-coloração das classes de grafos sem triangulo não isomorfo a um ciclo ímpar e bipartido cordal. Palavras-chave: Coloração por listas, Biclique, Coloração de arestas.Abstract: In graph coloring there are some versions of the vertex coloring and edge coloring problems. They can be defined using concepts like list coloring (to color graph elements given subsets of the set of colors) or coloring the elements of a graph such that there is no monochromatic structure. A graph G is said to be k-biclique edge-choosable if for any list assignment of colors to graph edges, which each list has size k, there is a coloring of E(G), that the edges can only use colors from theirs lists, such that there is no monochromatic biclique (maximal induced complete bipartite subgraph). If k is the smallest value such that G is k-biclique edge-choosable then k is the biclique choice index of G. Therefore we can define the k-biclique edge-choosability as the problem to decide if a given graph is k-biclique edge-choosable or not. In this dissertation we studied this problem by proving that triangle-free graphs not isomorphic to odd cycle are 2-star edge-choosable, the chordal bipartite are 2-biclique edge-choosable and showing a lower bound for the biclique choice index of power of cycles and power of paths. And we also show polynomial algorithms to compute a 2-biclique (star) edge-coloring for the graph classes triangle-free not isomorphic to odd cycle and chordal bipartite. Keywords: List coloring, biclique, edge coloring

NEOTROPICAL XENARTHRANS: a data set of occurrence of xenarthran species in the Neotropics

Xenarthrans—anteaters, sloths, and armadillos—have essential functions for ecosystem maintenance, such as insect control and nutrient cycling, playing key roles as ecosystem engineers. Because of habitat loss and fragmentation, hunting pressure, and conflicts with domestic dogs, these species have been threatened locally, regionally, or even across their full distribution ranges. The Neotropics harbor 21 species of armadillos, 10 anteaters, and 6 sloths. Our data set includes the families Chlamyphoridae (13), Dasypodidae (7), Myrmecophagidae (3), Bradypodidae (4), and Megalonychidae (2). We have no occurrence data on Dasypus pilosus (Dasypodidae). Regarding Cyclopedidae, until recently, only one species was recognized, but new genetic studies have revealed that the group is represented by seven species. In this data paper, we compiled a total of 42,528 records of 31 species, represented by occurrence and quantitative data, totaling 24,847 unique georeferenced records. The geographic range is from the southern United States, Mexico, and Caribbean countries at the northern portion of the Neotropics, to the austral distribution in Argentina, Paraguay, Chile, and Uruguay. Regarding anteaters, Myrmecophaga tridactyla has the most records (n = 5,941), and Cyclopes sp. have the fewest (n = 240). The armadillo species with the most data is Dasypus novemcinctus (n = 11,588), and the fewest data are recorded for Calyptophractus retusus (n = 33). With regard to sloth species, Bradypus variegatus has the most records (n = 962), and Bradypus pygmaeus has the fewest (n = 12). Our main objective with Neotropical Xenarthrans is to make occurrence and quantitative data available to facilitate more ecological research, particularly if we integrate the xenarthran data with other data sets of Neotropical Series that will become available very soon (i.e., Neotropical Carnivores, Neotropical Invasive Mammals, and Neotropical Hunters and Dogs). Therefore, studies on trophic cascades, hunting pressure, habitat loss, fragmentation effects, species invasion, and climate change effects will be possible with the Neotropical Xenarthrans data set. Please cite this data paper when using its data in publications. We also request that researchers and teachers inform us of how they are using these data

Brazilian Flora 2020: Leveraging the power of a collaborative scientific network

International audienceThe shortage of reliable primary taxonomic data limits the description of biological taxa and the understanding of biodiversity patterns and processes, complicating biogeographical, ecological, and evolutionary studies. This deficit creates a significant taxonomic impediment to biodiversity research and conservation planning. The taxonomic impediment and the biodiversity crisis are widely recognized, highlighting the urgent need for reliable taxonomic data. Over the past decade, numerous countries worldwide have devoted considerable effort to Target 1 of the Global Strategy for Plant Conservation (GSPC), which called for the preparation of a working list of all known plant species by 2010 and an online world Flora by 2020. Brazil is a megadiverse country, home to more of the world's known plant species than any other country. Despite that, Flora Brasiliensis, concluded in 1906, was the last comprehensive treatment of the Brazilian flora. The lack of accurate estimates of the number of species of algae, fungi, and plants occurring in Brazil contributes to the prevailing taxonomic impediment and delays progress towards the GSPC targets. Over the past 12 years, a legion of taxonomists motivated to meet Target 1 of the GSPC, worked together to gather and integrate knowledge on the algal, plant, and fungal diversity of Brazil. Overall, a team of about 980 taxonomists joined efforts in a highly collaborative project that used cybertaxonomy to prepare an updated Flora of Brazil, showing the power of scientific collaboration to reach ambitious goals. This paper presents an overview of the Brazilian Flora 2020 and provides taxonomic and spatial updates on the algae, fungi, and plants found in one of the world's most biodiverse countries. We further identify collection gaps and summarize future goals that extend beyond 2020. Our results show that Brazil is home to 46,975 native species of algae, fungi, and plants, of which 19,669 are endemic to the country. The data compiled to date suggests that the Atlantic Rainforest might be the most diverse Brazilian domain for all plant groups except gymnosperms, which are most diverse in the Amazon. However, scientific knowledge of Brazilian diversity is still unequally distributed, with the Atlantic Rainforest and the Cerrado being the most intensively sampled and studied biomes in the country. In times of “scientific reductionism”, with botanical and mycological sciences suffering pervasive depreciation in recent decades, the first online Flora of Brazil 2020 significantly enhanced the quality and quantity of taxonomic data available for algae, fungi, and plants from Brazil. This project also made all the information freely available online, providing a firm foundation for future research and for the management, conservation, and sustainable use of the Brazilian funga and flora

Growing knowledge: an overview of Seed Plant diversity in Brazil

Abstract An updated inventory of Brazilian seed plants is presented and offers important insights into the country's biodiversity. This work started in 2010, with the publication of the Plants and Fungi Catalogue, and has been updated since by more than 430 specialists working online. Brazil is home to 32,086 native Angiosperms and 23 native Gymnosperms, showing an increase of 3% in its species richness in relation to 2010. The Amazon Rainforest is the richest Brazilian biome for Gymnosperms, while the Atlantic Rainforest is the richest one for Angiosperms. There was a considerable increment in the number of species and endemism rates for biomes, except for the Amazon that showed a decrease of 2.5% of recorded endemics. However, well over half of Brazillian seed plant species (57.4%) is endemic to this territory. The proportion of life-forms varies among different biomes: trees are more expressive in the Amazon and Atlantic Rainforest biomes while herbs predominate in the Pampa, and lianas are more expressive in the Amazon, Atlantic Rainforest, and Pantanal. This compilation serves not only to quantify Brazilian biodiversity, but also to highlight areas where there information is lacking and to provide a framework for the challenge faced in conserving Brazil's unique and diverse flora