Rotulações graciosas e rotulações semifortes em grafos

Orientador: Christiane Neme CamposTese (doutorado) - Universidade Estadual de Campinas, Instituto de ComputaçãoResumo: Três problemas de rotulação em grafos são investigados nesta tese: a Conjetura das Árvores Graciosas, a Conjetura 1,2,3 e a Conjetura 1,2. Uma rotulação graciosa de um grafo simples G=(V(G),E(G)) é uma função injetora f de V(G) em {0,...,|E(G)|} tal que {|f(u)-f(v)|: uv em E(G)} = {1,...,|E(G)|}. A Conjetura das Árvores Graciosas, proposta por Rosa e Kotzig em 1967, afirma que toda árvore possui uma rotulação graciosa. Um problema relacionado à Conjetura das Árvores Graciosas consiste em determinar se, para todo vértice v de uma árvore T, existe uma rotulação graciosa de T que atribui o rótulo 0 a v. Árvores com tal propriedade são denominadas 0-rotativas. Nesta tese, apresentamos famílias infinitas de caterpillars 0-rotativos. Nossos resultados reforçam a conjetura de que todo caterpillar com diâmetro pelo menos cinco é 0-rotativo. Também investigamos uma rotulação graciosa mais restrita, chamada rotulação-alpha. Uma rotulação graciosa f de G é uma rotulação-alpha se existir um inteiro k, 0 <= k <= |E(G)|, tal que, para toda aresta uv em E(G), f(u) <= k < f(v) ou f(v) <= k < f(u). Nesta tese, apresentamos duas famílias de lobsters com grau máximo três que possuem rotulações-alpha. Nossos resultados contribuem para uma caracterização de todos os lobsters com grau máximo três que possuem rotulações-alpha. Na segunda parte desta tese, investigamos generalizações da Conjetura 1,2,3 e da Conjetura 1,2. Dado um grafo simples G = (V(G),E(G)) e um subconjunto L dos números reais, dizemos que uma função f de E(G) em L é uma L-rotulação de arestas de G e dizemos que uma função f da união de V(G) com E(G) em L é uma L-rotulação total de G. Para todo vértice v de G, a cor de v, C(v), é definida como a soma dos rótulos das arestas incidentes em v, se f for uma L-rotulação de arestas de G. Se f for uma L-rotulação total, C(v) é a soma dos rótulos das arestas incidentes no vértice v mais o valor f(v). O par (f,C) é uma L-rotulação de arestas semiforte (L-rotulação total semiforte) se f for uma rotulação de arestas (rotulação total) e C(u) for diferente de C(v) para quaisquer dois vértices adjacentes u,v de G. A Conjetura 1,2,3, proposta por Karónski et al. em 2004, afirma que todo grafo simples e conexo com pelo menos três vértices possui uma {1,2,3}-rotulação de arestas semiforte. A Conjetura 1,2, proposta por Przybylo e Wozniak em 2010, afirma que todo grafo simples possui uma {1,2}-rotulação total semiforte. Sejam a,b,c três reais distintos. Nesta tese, nós investigamos {a,b,c}-rotulações de arestas semifortes e {a,b}-rotulações totais semifortes para cinco famílias de grafos: as potências de caminho, as potências de ciclo, os grafos split, os grafos cobipartidos regulares e os grafos multipartidos completos. Provamos que essas famílias possuem tais rotulações para alguns valores reais a,b,c. Como corolário de nossos resultados, obtemos que a Conjetura 1,2,3 e a Conjetura 1,2 são verdadeiras para essas famílias. Além disso, também mostramos que nossos resultados em rotulações de arestas semifortes implicam resultados similares para outro problema de rotulação de arestas relacionadoAbstract: This thesis addresses three labelling problems on graphs: the Graceful Tree Conjecture, the 1,2,3-Conjecture, and the 1,2-Conjecture. A graceful labelling of a simple graph G=(V(G),E(G)) is an injective function f from V(G) to {0,...,|E(G)|} such that {|f(u)-f(v)| : uv in E(G)} = {1,...,|E(G)|}. The Graceful Tree Conjecture, posed by Rosa and Kotzig in 1967, states that every tree has a graceful labelling. A problem connected with the Graceful Tree Conjecture consists of determining whether, for every vertex v of a tree T, there exists a graceful labelling of T that assigns label 0 to v. Trees with such a property are called 0-rotatable. In this thesis, we present infinite families of 0-rotatable caterpillars. Our results reinforce a conjecture that states that every caterpillar with diameter at least five is 0-rotatable. We also investigate a stronger type of graceful labelling, called alpha-labelling. A graceful labelling f of G is an alpha-labelling if there exists an integer k with 0<= k <= |E(G)| such that, for each edge uv in E(G), either f(u) <= k < f(v) or f(v) <= k < f(u). In this thesis, we prove that the following families of lobsters have alpha-labellings: lobsters with maximum degree three, without Y-legs and with at most one forbidden ending; and lobsters T with a perfect matching M such that the contracted tree T/M has a balanced bipartition. These results point towards a characterization of all lobsters with maximum degree three that have alpha-labellings. In the second part of the thesis, we focus on generalizations of the 1,2,3-Conjecture and the 1,2-Conjecture. Given a simple graph G=(V(G),E(G)) and a subset L of real numbers, we call a function f from E(G) to L an L-edge-labelling of G, and we call a function f from V(G) union E(G) to L an L-total-labelling of G. For each vertex v of G, the colour of v, C(v), is defined as the sum of the labels of its incident edges, if f is an L-edge-labelling. If f is an L-total-labelling, C(v) is the sum of the labels of the edges incident with vertex v plus the label f(v). The pair (f,C) is a neighbour-distinguishing L-edge-labelling (neighbour-distinguishing L-total-labelling) if f is an edge-labelling (total-labelling) and C(u) is different from C(v), for every edge uv in E(G). The 1,2,3-Conjecture, posed by Kar\'onski et al. in 2004, states that every connected simple graph with at least three vertices has a neighbour-distinguishing {1,2,3}-edge-labelling. The 1,2-Conjecture, posed by Przybylo and Wozniak in 2010, states that every simple graph has a neighbour-distinguishing {1,2}-total-labelling. Let a,b,c be distinct real numbers. In this thesis, we investigate neighbour-distinguishing {a,b,c}-edge-labellings and neighbour-distinguishing {a,b}-total labellings for five families of graphs: powers of paths, powers of cycles, split graphs, regular cobipartite graphs and complete multipartite graphs. We prove that these families have such labellings for some real values a, b, and c. As a corollary of our results, we obtain that the 1,2,3-Conjecture and the 1,2-Conjecture are true for these families. Furthermore, we also show that our results on neighbour-distinguishing edge-labellings imply similar results on a closely related problem called detectable edge-labelling of graphsDoutoradoCiência da ComputaçãoDoutor em Ciência da Computação2014/16861-8FAPESPCAPE

Oceanus.

v. 26, no. 1 (1983

Sustainable development for traditional inhabitants of the Torres Strait region : proceedings of the Torres Strait Baseline Study Conference, Kewarra Beach, Cairns, Queensland, 19-23 November 1990

In July 1989 the Prime Minister of Australia, the Rt. Hon. R.J.L. Hawke, MP,announced, as part of his statement on the environment, which was later published as Our County, Our Future, that the Australian Government would fund a four year environmental study of the Torres Strait marine environment. This study, the Torres Strait Baseline Study, was instigated in response to concerns expressed by Torres Strait Islanders, commercial fishermen and scientists, about possible effects on the marine environment of the Torres Strait from mining operations in the Fly River catchment area of Papua New Guinea

Training Manual In the frame work of the project: DBT sponsored Three Months National Training in Molecular Biology and Biotechnology for Fisheries Professionals 2015-18

This is a limited edition of the CMFRI Training Manual provided to participants of the “DBT sponsored Three Months National Training in Molecular Biology and Biotechnology for Fisheries Professionals” organized by the Marine Biotechnology Division of Central Marine Fisheries Research Institute (CMFRI), from 2nd February 2015 - 31st March 2018

Sounding Sovereignty: The Politics of Presence in the Bismarck Archipelago

This dissertation examines socioecological rhythms in the Bismarck Archipelago of Papua New Guinea. Drawing on a year of ethnographic fieldwork in New Ireland Province between 2015 and 2016 and archival research conducted in 2017, I describe how the movement of bodies, spirits, and substances in and out of place engenders knowledge of distant pasts, social relations in the present, and the anticipation of diverse futures. I argue that it is possible—first through local ontologies and epistemologies, and second through an engaged environmental anthropology—to identify and negotiate the compositional forces which accelerate or delay such movements. In making this argument, I analyze a critical question asked by Mandak-speaking peoples of any new arrival (U pas mia?/From where have you come), and develop a second, supplemental question To whom do you owe the timing of your arrival? as a means of “sounding” spaces like the deep sea. In 2011, a multinational company known as Nautilus Minerals received permission from the Independent State of Papua New Guinea to commence the world’s first seafloor massive sulfide (SMS) mine in the deep Bismarck Sea. SMS deposits are rich in gold, copper, and other valuable metals, and have been identified in conjunction with deepwater hydrothermal vents along tectonic faults. In published literature and public fora, Nautilus has suggested the “offshore” location of the proposed site, along with its depth, darkness, pressure, and intermittent volcanism, afford it certain “natural” advantages over terrestrial mine sites. The Solwara 1 mine, they have argued, will cause “minimal environmental harm” and will be free of “landowner issues.” To this extent, Solwara 1 has been envisioned by the company, its consulting scientists, and the PNG government as a way of making development sustainable. Many people in New Ireland and its neighboring islands reject this assertion. Having experienced multiple waves of dispossession across successive generations, they are well aware that when foreign interests remove objects from their place, these objects often resist or refuse repatriation. Seabed mining not only poses a threat to sharks, tuna, and the endemic biodiversity present in the deep Bismarck Sea, but worse, it threatens the potential for social relations and self-determined futures that emerge out of such spaces. Through local meetings, legal channels, and social media, New Irelanders continue to resist the experimental nature of the mine. Considering this resistance, along with my own primary accountability to the people who have become my relatives in New Ireland and New Hanover (Lovongai), I offer in this dissertation a way of knowing Solwara 1 through Presence. As I describe it, Presence is both a spatiotemporal concept and a methodology. In the first sense, it serves as the logical ground for the critical questions asked of all new arrivals (mentioned above); it is the here and now from which the there and then can be imagined. As a research methodology, Presence makes possible a rhythmic political ecology—a way of experiencing and qualifying change within spaces that have been physically or discursively alienated from the peoples to whom we are (or should be) most accountable. Overall, Presence makes possible a critical redefinition of “environment”—one which accounts for the history of nurture by which potential relations are made to emerge at certain moments, or in other words, their nurtural history. This dissertation is divided into six chapters. In the first chapter, I describe the historical context of my arrival and fieldwork in the village of Tembin on New Ireland’s western shore. I include this for the reader as an answer to the question, From where have I come? In the second chapter, I draw on ethnographic evidence from a Mandak mortuary ceremony to describe the context and the work involved in producing a particular cultural object known as a mumu. While this particular mumu cannot be abstracted from the conditions of its own emergence without great consequence, my description of its production together with an appended timeline are intended to afford the reader a sense of the physical and conceptual grounds of what I am calling nurtural history. In the third chapter, I draw on theories of space, place, and knowledge from indigenous Pacific scholars and from philosopher Henri Lefebvre to formulate a rhythmic political ecology. The fourth and fifth chapters apply this approach to Deep Seabed Mining (DSM) and “Sharkcalling Culture,” respectively. Drawing on archival and ethnographic research, I consider in these chapters how distant places emerge into the present through both representation (by scientists, cultural tourists, and indigenous New Irelanders) and through “sounding,” or calling. In the final chapter, I consider how Solwara 1 has emerged as a social being in the Bismarck Archipelago, and how indigenous practices of sharkcalling and naming may be understood as assertions of continued sovereignty across local seas and in biksolwara—the big ocean

Subseafloor Biosphere Linked to Hydrothermal Systems: TAIGA Concept

Oceanography; Biogeosciences; Geochemistr

Material-based design computation

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Architecture, 2010.Cataloged from PDF version of thesis.Includes bibliographical references (p. 306-328).The institutionalized separation between form, structure and material, deeply embedded in modernist design theory, paralleled by a methodological partitioning between modeling, analysis and fabrication, resulted in geometric-driven form generation. Such prioritization of form over material was carried into the development and design logic of CAD. Today, under the imperatives and growing recognition of the failures and environmental liabilities of this approach, modern design culture is experiencing a shift to material aware design. Inspired by Nature's strategies where form generation is driven by maximal performance with minimal resources through local material property variation, the research reviews, proposes and develops models and processes for a material-based approach in computationally enabled form-generation. Material-based Design Computation is developed and proposed as a set of computational strategies supporting the integration of form, material and structure by incorporating physical form-finding strategies with digital analysis and fabrication. In this approach, material precedes shape, and it is the structuring of material properties as a function of structural and environmental performance that generates design form. The thesis proposes a unique approach to computationally-enabled form-finding procedures, and experimentally investigates how such processes contribute to novel ways of creating, distributing and depositing material forms. Variable Property Design is investigated as a theoretical and technical framework by which to model, analyze and fabricate objects with graduated properties designed to correspond to multiple and continuously varied functional constraints. The following methods were developed as the enabling mechanisms of Material Computation: Tiling Behavior & Digital Anisotropy, Finite Element Synthesis, and Material Pixels. In order to implement this approach as a fabrication process, a novel fabrication technology, termed Variable Property Rapid Prototyping has been developed, designed and patented. Among the potential contributions is the achievement of a high degree of customization through material heterogeneity as compared to conventional design of components and assemblies. Experimental designs employing suggested theoretical and technical frameworks, methods and techniques are presented, discussed and demonstrated. They support product customization, rapid augmentation and variable property fabrication. Developed as approximations of natural formation processes, these design experiments demonstrate the contribution and the potential future of a new design and research field.by Neri Oxman.Ph.D