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Polytopes And Graphs
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Author :Guillermo Pineda Villavicencio Publisher :Cambridge University Press ISBN 13 :1009257781 Total Pages :482 pages Book Rating :4.0/5 (92 download)
Book Synopsis Polytopes and Graphs by : Guillermo Pineda Villavicencio
Download or read book Polytopes and Graphs written by Guillermo Pineda Villavicencio and published by Cambridge University Press. This book was released on 2024-02-29 with total page 482 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces convex polytopes and their graphs, alongside the results and methodologies required to study them. It guides the reader from the basics to current research, presenting many open problems to facilitate the transition. The book includes results not previously found in other books, such as: the edge connectivity and linkedness of graphs of polytopes; the characterisation of their cycle space; the Minkowski decomposition of polytopes from the perspective of geometric graphs; Lei Xue's recent lower bound theorem on the number of faces of polytopes with a small number of vertices; and Gil Kalai's rigidity proof of the lower bound theorem for simplicial polytopes. This accessible introduction covers prerequisites from linear algebra, graph theory, and polytope theory. Each chapter concludes with exercises of varying difficulty, designed to help the reader engage with new concepts. These features make the book ideal for students and researchers new to the field.
Book Synopsis Mnogogranniki, Grafy, Optimizat︠s︡ii︠a︡ by : Vladimir Alekseevich Emelʹchev
Download or read book Mnogogranniki, Grafy, Optimizat︠s︡ii︠a︡ written by Vladimir Alekseevich Emelʹchev and published by . This book was released on 1984 with total page 423 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Scale-isometric Polytopal Graphs in Hypercubes and Cubic Lattices by : M. Deza
Download or read book Scale-isometric Polytopal Graphs in Hypercubes and Cubic Lattices written by M. Deza and published by Imperial College Press. This book was released on 2004 with total page 190 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph identifies polytopes that are combinatorially l1-embeddable, within interesting lists of polytopal graphs, i.e. such that corresponding polytopes are either prominent mathematically (regular partitions, root lattices, uniform polytopes and so on), or applicable in chemistry (fullerenes, polycycles, etc.). The embeddability, if any, provides applications to chemical graphs and, in the first case, it gives new combinatorial perspective to l2-prominent affine polytopal objects. The lists of polytopal graphs in the book come from broad areas of geometry, crystallography and graph theory. The book concentrates on such concise and, as much as possible, independent definitions. The scale-isometric embeddability the main unifying question, to which those lists are subjected is presented with the minimum of technicalities.
Book Synopsis Lectures on Polytopes by : Günter M. Ziegler
Download or read book Lectures on Polytopes written by Günter M. Ziegler and published by Springer Science & Business Media. This book was released on 2012-05-03 with total page 388 pages. Available in PDF, EPUB and Kindle. Book excerpt: Based on a graduate course at the Technische Universität, Berlin, these lectures present a wealth of material on the modern theory of convex polytopes. The straightforward exposition features many illustrations, and complete proofs for most theorems. With only linear algebra as a prerequisite, it takes the reader quickly from the basics to topics of recent research. The lectures introduce basic facts about polytopes, with an emphasis on methods that yield the results, discuss important examples and elegant constructions, and show the excitement of current work in the field. They will provide interesting and enjoyable reading for researchers as well as students.
Book Synopsis Symmetries in Graphs, Maps, and Polytopes by : Symmetries in graphs, maps, and polytopes
Download or read book Symmetries in Graphs, Maps, and Polytopes written by Symmetries in graphs, maps, and polytopes and published by . This book was released on 2022 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Convex Polytopes by : Branko Grünbaum
Download or read book Convex Polytopes written by Branko Grünbaum and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 561 pages. Available in PDF, EPUB and Kindle. Book excerpt: "The original edition [...] inspired a whole generation of grateful workers in polytope theory. Without it, it is doubtful whether many of the subsequent advances in the subject would have been made. The many seeds it sowed have since grown into healthy trees, with vigorous branches and luxuriant foliage. It is good to see it in print once again." --Peter McMullen, University College London
Book Synopsis Geometry of Cuts and Metrics by : Michel Marie Deza
Download or read book Geometry of Cuts and Metrics written by Michel Marie Deza and published by Springer. This book was released on 2009-11-12 with total page 580 pages. Available in PDF, EPUB and Kindle. Book excerpt: Cuts and metrics are well-known objects that arise - independently, but with many deep and fascinating connections - in diverse fields: in graph theory, combinatorial optimization, geometry of numbers, combinatorial matrix theory, statistical physics, VLSI design etc. This book presents a wealth of results, from different mathematical disciplines, in a unified comprehensive manner, and establishes new and old links, which cannot be found elsewhere. It provides a unique and invaluable source for researchers and graduate students. From the Reviews: "This book is definitely a milestone in the literature of integer programming and combinatorial optimization. It draws from the Interdisciplinarity of these fields [...]. With knowledge about the relevant terms, one can enjoy special subsections without being entirely familiar with the rest of the chapter. This makes it not only an interesting research book but even a dictionary. [...] The longer one works with it, the more beautiful it becomes." Optima 56, 1997.
Book Synopsis Lectures on Polytopes by : Günter M. Ziegler
Download or read book Lectures on Polytopes written by Günter M. Ziegler and published by Springer. This book was released on 2012-05-03 with total page 388 pages. Available in PDF, EPUB and Kindle. Book excerpt: Based on a graduate course at the Technische Universität, Berlin, these lectures present a wealth of material on the modern theory of convex polytopes. The straightforward exposition features many illustrations, and complete proofs for most theorems. With only linear algebra as a prerequisite, it takes the reader quickly from the basics to topics of recent research. The lectures introduce basic facts about polytopes, with an emphasis on methods that yield the results, discuss important examples and elegant constructions, and show the excitement of current work in the field. They will provide interesting and enjoyable reading for researchers as well as students.
Book Synopsis Polytopes and Discrete Geometry by : Gabriel Cunningham
Download or read book Polytopes and Discrete Geometry written by Gabriel Cunningham and published by American Mathematical Soc.. This book was released on 2021-04-06 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: The papers showcase the breadth of discrete geometry through many new methods and results in a variety of topics. Also included are survey articles on some important areas of active research. This volume is aimed at researchers in discrete and convex geometry and researchers who work with abstract polytopes or string C C-groups. It is also aimed at early career mathematicians, including graduate students and postdoctoral fellows, to give them a glimpse of the variety and beauty of these research areas. Topics covered in this volume include: the combinatorics, geometry, and symmetries of convex polytopes; tilings; discrete point sets; the combinatorics of Eulerian posets and interval posets; symmetries of surfaces and maps on surfaces; self-dual polytopes; string C C-groups; hypertopes; and graph coloring.
Book Synopsis Equipartite Polytopes and Graphs by : Branko Grünbaum
Download or read book Equipartite Polytopes and Graphs written by Branko Grünbaum and published by . This book was released on 2004 with total page 33 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Polytopes - Combinations and Computation by : Gil Kalai
Download or read book Polytopes - Combinations and Computation written by Gil Kalai and published by Birkhäuser. This book was released on 2012-12-06 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: Questions that arose from linear programming and combinatorial optimization have been a driving force for modern polytope theory, such as the diameter questions motivated by the desire to understand the complexity of the simplex algorithm, or the need to study facets for use in cutting plane procedures. In addition, algorithms now provide the means to computationally study polytopes, to compute their parameters such as flag vectors, graphs and volumes, and to construct examples of large complexity. The papers of this volume thus display a wide panorama of connections of polytope theory with other fields. Areas such as discrete and computational geometry, linear and combinatorial optimization, and scientific computing have contributed a combination of questions, ideas, results, algorithms and, finally, computer programs.
Download or read book Polytopes written by Tibor Bisztriczky and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 515 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this volume is to reinforce the interaction between the three main branches (abstract, convex and computational) of the theory of polytopes. The articles include contributions from many of the leading experts in the field, and their topics of concern are expositions of recent results and in-depth analyses of the development (past and future) of the subject. The subject matter of the book ranges from algorithms for assignment and transportation problems to the introduction of a geometric theory of polyhedra which need not be convex. With polytopes as the main topic of interest, there are articles on realizations, classifications, Eulerian posets, polyhedral subdivisions, generalized stress, the Brunn--Minkowski theory, asymptotic approximations and the computation of volumes and mixed volumes. For researchers in applied and computational convexity, convex geometry and discrete geometry at the graduate and postgraduate levels.
Book Synopsis Geometric Graphs and Arrangements by : Stefan Felsner
Download or read book Geometric Graphs and Arrangements written by Stefan Felsner and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 179 pages. Available in PDF, EPUB and Kindle. Book excerpt: Among the intuitively appealing aspects of graph theory is its close connection to drawings and geometry. The development of computer technology has become a source of motivation to reconsider these connections, in particular geometric graphs are emerging as a new subfield of graph theory. Arrangements of points and lines are the objects for many challenging problems and surprising solutions in combinatorial geometry. The book is a collection of beautiful and partly very recent results from the intersection of geometry, graph theory and combinatorics.
Book Synopsis An Introduction to Convex Polytopes by : Arne Brondsted
Download or read book An Introduction to Convex Polytopes written by Arne Brondsted and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 168 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this book is to introduce the reader to the fascinating world of convex polytopes. The highlights of the book are three main theorems in the combinatorial theory of convex polytopes, known as the Dehn-Sommerville Relations, the Upper Bound Theorem and the Lower Bound Theorem. All the background information on convex sets and convex polytopes which is m~eded to under stand and appreciate these three theorems is developed in detail. This background material also forms a basis for studying other aspects of polytope theory. The Dehn-Sommerville Relations are classical, whereas the proofs of the Upper Bound Theorem and the Lower Bound Theorem are of more recent date: they were found in the early 1970's by P. McMullen and D. Barnette, respectively. A famous conjecture of P. McMullen on the charac terization off-vectors of simplicial or simple polytopes dates from the same period; the book ends with a brief discussion of this conjecture and some of its relations to the Dehn-Sommerville Relations, the Upper Bound Theorem and the Lower Bound Theorem. However, the recent proofs that McMullen's conditions are both sufficient (L. J. Billera and C. W. Lee, 1980) and necessary (R. P. Stanley, 1980) go beyond the scope of the book. Prerequisites for reading the book are modest: standard linear algebra and elementary point set topology in [R1d will suffice.
Book Synopsis Graphs and Hypergraphs by : Claude Berge
Download or read book Graphs and Hypergraphs written by Claude Berge and published by . This book was released on 1973 with total page 556 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Oriented Matroids by : Anders Björner
Download or read book Oriented Matroids written by Anders Björner and published by Cambridge University Press. This book was released on 1999-11-18 with total page 564 pages. Available in PDF, EPUB and Kindle. Book excerpt: First comprehensive, accessible account; second edition has expanded bibliography and a new appendix surveying recent research.
Book Synopsis Graphs and Dual Graphs of Abstract Polytopes by : Ilan Eldar
Download or read book Graphs and Dual Graphs of Abstract Polytopes written by Ilan Eldar and published by . This book was released on 1971 with total page 36 pages. Available in PDF, EPUB and Kindle. Book excerpt: