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Author: Seok-Hee Hong
Publisher: Springer Nature
ISBN: 9811565333
Category : Computers
Languages : en
Pages : 269
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Book Description
This book is the first general and extensive review on the algorithmics and mathematical results of beyond planar graphs. Most real-world data sets are relational and can be modelled as graphs consisting of vertices and edges. Planar graphs are fundamental for both graph theory and graph algorithms and are extensively studied. Structural properties and fundamental algorithms for planar graphs have been discovered. However, most real-world graphs, such as social networks and biological networks, are non-planar. To analyze and visualize such real-world networks, it is necessary to solve fundamental mathematical and algorithmic research questions on sparse non-planar graphs, called beyond planar graphs.This book is based on the National Institute of Informatics (NII) Shonan Meeting on algorithmics on beyond planar graphs held in Japan in November, 2016. The book consists of 13 chapters that represent recent advances in various areas of beyond planar graph research. The main aims and objectives of this book include 1) to timely provide a state-of-the-art survey and a bibliography on beyond planar graphs; 2) to set the research agenda on beyond planar graphs by identifying fundamental research questions and new research directions; and 3) to foster cross-disciplinary research collaboration between computer science (graph drawing and computational geometry) and mathematics (graph theory and combinatorics). New algorithms for beyond planar graphs will be in high demand by practitioners in various application domains to solve complex visualization problems. This book therefore will be a valuable resource for researchers in graph theory, algorithms, and theoretical computer science, and will stimulate further deep scientific investigations into many areas of beyond planar graphs.
Author: Seok-Hee Hong
Publisher: Springer Nature
ISBN: 9811565333
Category : Computers
Languages : en
Pages : 269
Get Book Here
Book Description
This book is the first general and extensive review on the algorithmics and mathematical results of beyond planar graphs. Most real-world data sets are relational and can be modelled as graphs consisting of vertices and edges. Planar graphs are fundamental for both graph theory and graph algorithms and are extensively studied. Structural properties and fundamental algorithms for planar graphs have been discovered. However, most real-world graphs, such as social networks and biological networks, are non-planar. To analyze and visualize such real-world networks, it is necessary to solve fundamental mathematical and algorithmic research questions on sparse non-planar graphs, called beyond planar graphs.This book is based on the National Institute of Informatics (NII) Shonan Meeting on algorithmics on beyond planar graphs held in Japan in November, 2016. The book consists of 13 chapters that represent recent advances in various areas of beyond planar graph research. The main aims and objectives of this book include 1) to timely provide a state-of-the-art survey and a bibliography on beyond planar graphs; 2) to set the research agenda on beyond planar graphs by identifying fundamental research questions and new research directions; and 3) to foster cross-disciplinary research collaboration between computer science (graph drawing and computational geometry) and mathematics (graph theory and combinatorics). New algorithms for beyond planar graphs will be in high demand by practitioners in various application domains to solve complex visualization problems. This book therefore will be a valuable resource for researchers in graph theory, algorithms, and theoretical computer science, and will stimulate further deep scientific investigations into many areas of beyond planar graphs.
Author: Oscar Levin
Publisher: Createspace Independent Publishing Platform
ISBN: 9781534970748
Category :
Languages : en
Pages : 342
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Book Description
This gentle introduction to discrete mathematics is written for first and second year math majors, especially those who intend to teach. The text began as a set of lecture notes for the discrete mathematics course at the University of Northern Colorado. This course serves both as an introduction to topics in discrete math and as the "introduction to proof" course for math majors. The course is usually taught with a large amount of student inquiry, and this text is written to help facilitate this. Four main topics are covered: counting, sequences, logic, and graph theory. Along the way proofs are introduced, including proofs by contradiction, proofs by induction, and combinatorial proofs. The book contains over 360 exercises, including 230 with solutions and 130 more involved problems suitable for homework. There are also Investigate! activities throughout the text to support active, inquiry based learning. While there are many fine discrete math textbooks available, this text has the following advantages: It is written to be used in an inquiry rich course. It is written to be used in a course for future math teachers. It is open source, with low cost print editions and free electronic editions.
Author: Fabrizio Frati
Publisher: Springer
ISBN: 3319739158
Category : Computers
Languages : en
Pages : 636
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Book Description
This book constitutes revised selected papers from the 25th International Symposium on Graph Drawing and Network Visualization, GD 2017, held in Boston, MA, USA, in September 2017.The 34 full and 9 short papers presented in this volume were carefully reviewed and selected from 87 submissions. Also included in this book are 2 abstracts of keynote presentations, 16 poster abstracts, and 1 contest report. The papers are organized in topical sections named: straight-line representations; obstacles and visibility; topological graph theory; orthogonal representations and book embeddings; evaluations; tree drawings; graph layout designs; point-set embeddings; special representations; and beyond planarity.
Author: László Lovász
Publisher: Springer Science & Business Media
ISBN: 0387217770
Category : Mathematics
Languages : en
Pages : 344
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Book Description
Aimed at undergraduate mathematics and computer science students, this book is an excellent introduction to a lot of problems of discrete mathematics. It discusses a number of selected results and methods, mostly from areas of combinatorics and graph theory, and it uses proofs and problem solving to help students understand the solutions to problems. Numerous examples, figures, and exercises are spread throughout the book.
Author: Stefan Felsner
Publisher: Springer Science & Business Media
ISBN: 3322803031
Category : Mathematics
Languages : en
Pages : 179
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Book Description
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.
Author: Cun-Quan Zhang
Publisher: CRC Press
ISBN: 9780824797904
Category : Mathematics
Languages : en
Pages : 402
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Book Description
Focuses on classical problems in graph theory, including the 5-flow conjectures, the edge-3-colouring conjecture, the 3-flow conjecture and the cycle double cover conjecture. The text highlights the interrelationships between graph colouring, integer flow, cycle covers and graph minors. It also concentrates on graph theoretical methods and results.
Author: Arthur Benjamin
Publisher: Princeton University Press
ISBN: 0691175632
Category : Mathematics
Languages : en
Pages : 338
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Book Description
The history, formulas, and most famous puzzles of graph theory Graph theory goes back several centuries and revolves around the study of graphs—mathematical structures showing relations between objects. With applications in biology, computer science, transportation science, and other areas, graph theory encompasses some of the most beautiful formulas in mathematics—and some of its most famous problems. The Fascinating World of Graph Theory explores the questions and puzzles that have been studied, and often solved, through graph theory. This book looks at graph theory's development and the vibrant individuals responsible for the field's growth. Introducing fundamental concepts, the authors explore a diverse plethora of classic problems such as the Lights Out Puzzle, and each chapter contains math exercises for readers to savor. An eye-opening journey into the world of graphs, The Fascinating World of Graph Theory offers exciting problem-solving possibilities for mathematics and beyond.
Author: Bojan Mohar
Publisher: Johns Hopkins University Press
ISBN: 9780801866890
Category : Mathematics
Languages : en
Pages : 0
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Book Description
Graph theory is one of the fastest growing branches of mathematics. Until recently, it was regarded as a branch of combinatorics and was best known by the famous four-color theorem stating that any map can be colored using only four colors such that no two bordering countries have the same color. Now graph theory is an area of its own with many deep results and beautiful open problems. Graph theory has numerous applications in almost every field of science and has attracted new interest because of its relevance to such technological problems as computer and telephone networking and, of course, the internet. In this new book in the Johns Hopkins Studies in the Mathematical Science series, Bojan Mohar and Carsten Thomassen look at a relatively new area of graph theory: that associated with curved surfaces. Graphs on surfaces form a natural link between discrete and continuous mathematics. The book provides a rigorous and concise introduction to graphs on surfaces and surveys some of the recent developments in this area. Among the basic results discussed are Kuratowski's theorem and other planarity criteria, the Jordan Curve Theorem and some of its extensions, the classification of surfaces, and the Heffter-Edmonds-Ringel rotation principle, which makes it possible to treat graphs on surfaces in a purely combinatorial way. The genus of a graph, contractability of cycles, edge-width, and face-width are treated purely combinatorially, and several results related to these concepts are included. The extension by Robertson and Seymour of Kuratowski's theorem to higher surfaces is discussed in detail, and a shorter proof is presented. The book concludes with a survey of recent developments on coloring graphs on surfaces.
Author: Michael Kaufmann
Publisher: Springer
ISBN: 3540449698
Category : Mathematics
Languages : en
Pages : 325
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Book Description
Graph drawing comprises all aspects of visualizing structural relations between objects. The range of topics dealt with extends from graph theory, graph algorithms, geometry, and topology to visual languages, visual perception, and information visualization, and to computer-human interaction and graphics design. This monograph gives a systematic overview of graph drawing and introduces the reader gently to the state of the art in the area. The presentation concentrates on algorithmic aspects, with an emphasis on interesting visualization problems with elegant solutions. Much attention is paid to a uniform style of writing and presentation, consistent terminology, and complementary coverage of the relevant issues throughout the 10 chapters. This tutorial is ideally suited as an introduction for newcomers to graph drawing. Ambitioned practitioners and researchers active in the area will find it a valuable source of reference and information.
Author: Alexander Soifer
Publisher: Springer Science & Business Media
ISBN: 0387746420
Category : Mathematics
Languages : en
Pages : 619
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Book Description
This book provides an exciting history of the discovery of Ramsey Theory, and contains new research along with rare photographs of the mathematicians who developed this theory, including Paul Erdös, B.L. van der Waerden, and Henry Baudet.
