Convexity And Graph Theory
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Convexity And Graph Theory
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Author : M. Rosenfeld
language : en
Publisher: Elsevier
Release Date : 1984-01-01
Convexity And Graph Theory written by M. Rosenfeld and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 1984-01-01 with Mathematics categories.
Among the participants discussing recent trends in their respective fields and in areas of common interest in these proceedings are such world-famous geometers as H.S.M. Coxeter, L. Danzer, D.G. Larman and J.M. Wills, and equally famous graph-theorists B. Bollobás, P. Erdös and F. Harary. In addition to new results in both geometry and graph theory, this work includes articles involving both of these two fields, for instance ``Convexity, Graph Theory and Non-Negative Matrices'', ``Weakly Saturated Graphs are Rigid'', and many more. The volume covers a broad spectrum of topics in graph theory, geometry, convexity, and combinatorics. The book closes with a number of abstracts and a collection of open problems raised during the conference.
Introduction To Graph Convexity
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Author : Júlio Araújo
language : en
Publisher: Springer Nature
Release Date : 2025-05-12
Introduction To Graph Convexity written by Júlio Araújo and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-05-12 with Mathematics categories.
This book focuses on the computational aspects of graph convexity, with a particular emphasis on path convexity within graphs. It provides a thoughtful introduction to this emerging research field, which originated by adapting concepts from convex geometry to combinatorics and has experienced substantial growth. The book starts with an introduction of fundamental convexity concepts and then proceeds to discuss convexity parameters. These parameters fall into two categories: one derived from abstract convexity studies and another motivated by computational complexity. Subsequent chapters explore geometric convexity within graphs, examining various graph classes such as interval graphs, proper interval graphs, cographs, chordal graphs, and strongly chordal graphs. The text concludes with a study of the computation of convexity parameters across different convexity types, including practical applications in areas like game theory. Compact and straightforward, this work serves as an ideal entry point for students and researchers interested in pursuing further research in the field of convexity. The English translation of this book, originally in Portuguese, was facilitated by artificial intelligence. The content was later revised by the authors for accuracy.
Geodesic Convexity In Graphs
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Author : Ignacio M. Pelayo
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-09-06
Geodesic Convexity In Graphs written by Ignacio M. Pelayo and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-09-06 with Mathematics categories.
Geodesic Convexity in Graphs is devoted to the study of the geodesic convexity on finite, simple, connected graphs. The first chapter includes the main definitions and results on graph theory, metric graph theory and graph path convexities. The following chapters focus exclusively on the geodesic convexity, including motivation and background, specific definitions, discussion and examples, results, proofs, exercises and open problems. The main and most studied parameters involving geodesic convexity in graphs are both the geodetic and the hull number which are defined as the cardinality of minimum geodetic and hull set, respectively. This text reviews various results, obtained during the last one and a half decade, relating these two invariants and some others such as convexity number, Steiner number, geodetic iteration number, Helly number, and Caratheodory number to a wide range a contexts, including products, boundary-type vertex sets, and perfect graph families. This monograph can serve as a supplement to a half-semester graduate course in geodesic convexity but is primarily a guide for postgraduates and researchers interested in topics related to metric graph theory and graph convexity theory.
Combinatorial Convexity
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Author : Imre Bárány
language : en
Publisher: American Mathematical Soc.
Release Date : 2021-11-04
Combinatorial Convexity written by Imre Bárány and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-11-04 with Education categories.
This book is about the combinatorial properties of convex sets, families of convex sets in finite dimensional Euclidean spaces, and finite points sets related to convexity. This area is classic, with theorems of Helly, Carathéodory, and Radon that go back more than a hundred years. At the same time, it is a modern and active field of research with recent results like Tverberg's theorem, the colourful versions of Helly and Carathéodory, and the (p,q) (p,q) theorem of Alon and Kleitman. As the title indicates, the topic is convexity and geometry, and is close to discrete mathematics. The questions considered are frequently of a combinatorial nature, and the proofs use ideas from geometry and are often combined with graph and hypergraph theory. The book is intended for students (graduate and undergraduate alike), but postdocs and research mathematicians will also find it useful. It can be used as a textbook with short chapters, each suitable for a one- or two-hour lecture. Not much background is needed: basic linear algebra and elements of (hyper)graph theory as well as some mathematical maturity should suffice.
A Course In Convexity
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Author : Alexander Barvinok
language : en
Publisher: American Mathematical Soc.
Release Date : 2002-11-19
A Course In Convexity written by Alexander Barvinok and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-11-19 with Mathematics categories.
Convexity is a simple idea that manifests itself in a surprising variety of places. This fertile field has an immensely rich structure and numerous applications. Barvinok demonstrates that simplicity, intuitive appeal, and the universality of applications make teaching (and learning) convexity a gratifying experience. The book will benefit both teacher and student: It is easy to understand, entertaining to the reader, and includes many exercises that vary in degree of difficulty. Overall, the author demonstrates the power of a few simple unifying principles in a variety of pure and applied problems. The prerequisites are minimal amounts of linear algebra, analysis, and elementary topology, plus basic computational skills. Portions of the book could be used by advanced undergraduates. As a whole, it is designed for graduate students interested in mathematical methods, computer science, electrical engineering, and operations research. The book will also be of interest to research mathematicians, who will find some results that are recent, some that are new, and many known results that are discussed from a new perspective.
Distance In Graphs
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Author : Fred Buckley
language : en
Publisher: Addison Wesley Publishing Company
Release Date : 1990-01-21
Distance In Graphs written by Fred Buckley and has been published by Addison Wesley Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990-01-21 with Mathematics categories.
Convex Optimization
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Author : Stephen P. Boyd
language : en
Publisher: Cambridge University Press
Release Date : 2004-03-08
Convex Optimization written by Stephen P. Boyd and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-03-08 with Business & Economics categories.
Convex optimization problems arise frequently in many different fields. This book provides a comprehensive introduction to the subject, and shows in detail how such problems can be solved numerically with great efficiency. The book begins with the basic elements of convex sets and functions, and then describes various classes of convex optimization problems. Duality and approximation techniques are then covered, as are statistical estimation techniques. Various geometrical problems are then presented, and there is detailed discussion of unconstrained and constrained minimization problems, and interior-point methods. The focus of the book is on recognizing convex optimization problems and then finding the most appropriate technique for solving them. It contains many worked examples and homework exercises and will appeal to students, researchers and practitioners in fields such as engineering, computer science, mathematics, statistics, finance and economics.
Convexity From The Geometric Point Of View
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Author : Vitor Balestro
language : en
Publisher: Springer Nature
Release Date : 2024-07-14
Convexity From The Geometric Point Of View written by Vitor Balestro and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-07-14 with Mathematics categories.
This text gives a comprehensive introduction to the “common core” of convex geometry. Basic concepts and tools which are present in all branches of that field are presented with a highly didactic approach. Mainly directed to graduate and advanced undergraduates, the book is self-contained in such a way that it can be read by anyone who has standard undergraduate knowledge of analysis and of linear algebra. Additionally, it can be used as a single reference for a complete introduction to convex geometry, and the content coverage is sufficiently broad that the reader may gain a glimpse of the entire breadth of the field and various subfields. The book is suitable as a primary text for courses in convex geometry and also in discrete geometry (including polytopes). It is also appropriate for survey type courses in Banach space theory, convex analysis, differential geometry, and applications of measure theory. Solutions to all exercises are available to instructors who adopt the text for coursework. Most chapters use the same structure with the first part presenting theory and the next containing a healthy range of exercises. Some of the exercises may even be considered as short introductions to ideas which are not covered in the theory portion. Each chapter has a notes section offering a rich narrative to accompany the theory, illuminating the development of ideas, and providing overviews to the literature concerning the covered topics. In most cases, these notes bring the reader to the research front. The text includes many figures that illustrate concepts and some parts of the proofs, enabling the reader to have a better understanding of the geometric meaning of the ideas. An appendix containing basic (and geometric) measure theory collects useful information for convex geometers.
The Seventh European Conference On Combinatorics Graph Theory And Applications
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Author : Jaroslav Nešetřil
language : en
Publisher: Springer Science & Business Media
Release Date : 2014-01-18
The Seventh European Conference On Combinatorics Graph Theory And Applications written by Jaroslav Nešetřil and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-18 with Mathematics categories.
In the tradition of EuroComb'01 (Barcelona), Eurocomb'03 (Prague), EuroComb'05 (Berlin), Eurocomb'07 (Seville), Eurocomb'09 (Bordeaux), and Eurocomb'11 (Budapest), this volume covers recent advances in combinatorics and graph theory including applications in other areas of mathematics, computer science and engineering. Topics include, but are not limited to: Algebraic combinatorics, combinatorial geometry, combinatorial number theory, combinatorial optimization, designs and configurations, enumerative combinatorics, extremal combinatorics, ordered sets, random methods, topological combinatorics.
Handbook Of Convex Geometry
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Author : Bozzano G Luisa
language : en
Publisher: Elsevier
Release Date : 2014-06-28
Handbook Of Convex Geometry written by Bozzano G Luisa and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-06-28 with Mathematics categories.
Handbook of Convex Geometry, Volume A offers a survey of convex geometry and its many ramifications and relations with other areas of mathematics, including convexity, geometric inequalities, and convex sets. The selection first offers information on the history of convexity, characterizations of convex sets, and mixed volumes. Topics include elementary convexity, equality in the Aleksandrov-Fenchel inequality, mixed surface area measures, characteristic properties of convex sets in analysis and differential geometry, and extensions of the notion of a convex set. The text then reviews the standard isoperimetric theorem and stability of geometric inequalities. The manuscript takes a look at selected affine isoperimetric inequalities, extremum problems for convex discs and polyhedra, and rigidity. Discussions focus on include infinitesimal and static rigidity related to surfaces, isoperimetric problem for convex polyhedral, bounds for the volume of a convex polyhedron, curvature image inequality, Busemann intersection inequality and its relatives, and Petty projection inequality. The book then tackles geometric algorithms, convexity and discrete optimization, mathematical programming and convex geometry, and the combinatorial aspects of convex polytopes. The selection is a valuable source of data for mathematicians and researchers interested in convex geometry.