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Graph theory. --- Théorie des graphes --- Graph theory --- Théorie des graphes --- ELSEVIER-B EPUB-LIV-FT

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Graph theory is a flourishing discipline containing a body of beautiful and powerful theorems of wide applicability. Its explosive growth in recent years is mainly due to its role as an essential structure underpinning modern applied mathematics computer science, combinatorial optimization, and operations research in particular but also to its increasing application in the more applied sciences. The versatility of graphs makes them indispensable tools in the design and analysis of communication networks, for instance. The primary aim of this book is to present a coherent introduction to the subject, suitable as a textbook for advanced undergraduate and beginning graduate students in mathematics and computer science. It provides a systematic treatment of the theory of graphs without sacrificing its intuitive and aesthetic appeal. Commonly used proof techniques are described and illustrated, and a wealth of exercises - of varying levels of difficulty - are provided to help the reader master the techniques and reinforce their grasp of the material. A second objective is to serve as an introduction to research in graph theory. To this end, sections on more advanced topics are included, and a number of interesting and challenging open problems are highlighted and discussed in some detail. Despite this more advanced material, the book has been organized in such a way that an introductory course on graph theory can be based on the first few sections of selected chapters.

Graph theory. --- Graph theory --- Théorie des graphes --- EPUB-LIV-FT LIVMATHE SPRINGER-B --- Graphes, Théorie des.

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Discrete mathematics --- 519.1 --- Combinatorics. Graph theory --- 519.1 Combinatorics. Graph theory --- Graph theory --- Théorie des graphes --- Congresses --- Congrès --- Graphes, Théorie des

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This introductory text in graph theory focuses on partial cubes, which are graphs that are isometrically embeddable into hypercubes of an arbitrary dimension, as well as bipartite graphs, and cubical graphs. This branch of graph theory has developed rapidly during the past three decades, producing exciting results and establishing links to other branches of mathematics.   Currently, Graphs and Cubes is the only book available on the market that presents a comprehensive coverage of cubical graph and partial cube theories.  Many exercises, along with historical notes, are included at the end of every chapter, and readers are encouraged to explore the exercises fully, and use them as a basis for research projects.   The prerequisites for this text include familiarity with basic mathematical concepts and methods on the level of undergraduate courses in discrete mathematics, linear algebra, group theory, and topology of Euclidean spaces. While the book is intended for lower-division graduate students in mathematics, it will be of interest to a much wider audience; because of their rich structural properties, partial cubes appear in theoretical computer science, coding theory, genetics, and even the political and social sciences.

Statistical science --- Discrete mathematics --- Mathematical statistics --- Mathematics --- grafieken --- statistiek --- wiskunde --- Graph theory --- Geometry --- Théorie des graphes --- Graphic methods --- EPUB-LIV-FT LIVMATHE LIVSTATI SPRINGER-B

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This is the first volume of a subseries of the Lecture Notes in Mathematics which will appear randomly over the next years. Each volume will describe some important topic in the theory or applications of Lévy processes and pay tribute to the state of the art of this rapidly evolving subject with special emphasis on the non-Brownian world. The three expository articles of this first volume have been chosen to reflect the breadth of the area of Lévy processes. The first article by Ken-iti Sato characterizes extensions of the class of selfdecomposable distributions on Rd. The second article by Thomas Duquesne discusses Hausdorff and packing measures of stable trees. The third article by Oleg Reichmann and Christoph Schwab presents numerical solutions to Kolmogoroff equations, which arise for instance in financial engineering, when Lévy or additive processes model the dynamics of the risky assets.

Lévy processes --- Branching processes --- Trees (Graph theory) --- Lévy, Processus de --- Processus ramifiés --- Arbres (Théorie des graphes) --- Lévy processes --- Lévy, Processus de --- Processus ramifiés --- Arbres (Théorie des graphes) --- EPUB-LIV-FT LIVMATHE LIVSTATI SPRINGER-B