Beyond Planar Graphs

Beyond Planar Graphs

Author: Seok-Hee Hong

Publisher: Springer Nature

Published: 2020-09-30

Total Pages: 270

ISBN-13: 9811565333

DOWNLOAD EBOOK

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.


Book Synopsis Beyond Planar Graphs by : Seok-Hee Hong

Download or read book Beyond Planar Graphs written by Seok-Hee Hong and published by Springer Nature. This book was released on 2020-09-30 with total page 270 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Discrete Mathematics

Discrete Mathematics

Author: Oscar Levin

Publisher: Createspace Independent Publishing Platform

Published: 2018-07-30

Total Pages: 238

ISBN-13: 9781724572639

DOWNLOAD EBOOK

Note: This is a custom edition of Levin's full Discrete Mathematics text, arranged specifically for use in a discrete math course for future elementary and middle school teachers. (It is NOT a new and updated edition of the main text.)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.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.


Book Synopsis Discrete Mathematics by : Oscar Levin

Download or read book Discrete Mathematics written by Oscar Levin and published by Createspace Independent Publishing Platform. This book was released on 2018-07-30 with total page 238 pages. Available in PDF, EPUB and Kindle. Book excerpt: Note: This is a custom edition of Levin's full Discrete Mathematics text, arranged specifically for use in a discrete math course for future elementary and middle school teachers. (It is NOT a new and updated edition of the main text.)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.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.

Planar Graphs

Planar Graphs

Author: Takao Nishizeki

Publisher: Courier Corporation

Published: 2008-01-01

Total Pages: 242

ISBN-13: 048646671X

DOWNLOAD EBOOK

This text features most of the important theorems and algorithms for planar graphs. Suitable as a textbook, it is also useful for researchers and includes an extensive reference section. 1988 edition.


Book Synopsis Planar Graphs by : Takao Nishizeki

Download or read book Planar Graphs written by Takao Nishizeki and published by Courier Corporation. This book was released on 2008-01-01 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text features most of the important theorems and algorithms for planar graphs. Suitable as a textbook, it is also useful for researchers and includes an extensive reference section. 1988 edition.

Planar Graphs

Planar Graphs

Author: T. Nishizeki

Publisher: Elsevier

Published: 1988-04-01

Total Pages: 247

ISBN-13: 008086774X

DOWNLOAD EBOOK

Collected in this volume are most of the important theorems and algorithms currently known for planar graphs, together with constructive proofs for the theorems. Many of the algorithms are written in Pidgin PASCAL, and are the best-known ones; the complexities are linear or 0(nlogn). The first two chapters provide the foundations of graph theoretic notions and algorithmic techniques. The remaining chapters discuss the topics of planarity testing, embedding, drawing, vertex- or edge-coloring, maximum independence set, subgraph listing, planar separator theorem, Hamiltonian cycles, and single- or multicommodity flows. Suitable for a course on algorithms, graph theory, or planar graphs, the volume will also be useful for computer scientists and graph theorists at the research level. An extensive reference section is included.


Book Synopsis Planar Graphs by : T. Nishizeki

Download or read book Planar Graphs written by T. Nishizeki and published by Elsevier. This book was released on 1988-04-01 with total page 247 pages. Available in PDF, EPUB and Kindle. Book excerpt: Collected in this volume are most of the important theorems and algorithms currently known for planar graphs, together with constructive proofs for the theorems. Many of the algorithms are written in Pidgin PASCAL, and are the best-known ones; the complexities are linear or 0(nlogn). The first two chapters provide the foundations of graph theoretic notions and algorithmic techniques. The remaining chapters discuss the topics of planarity testing, embedding, drawing, vertex- or edge-coloring, maximum independence set, subgraph listing, planar separator theorem, Hamiltonian cycles, and single- or multicommodity flows. Suitable for a course on algorithms, graph theory, or planar graphs, the volume will also be useful for computer scientists and graph theorists at the research level. An extensive reference section is included.

Planar Graphs

Planar Graphs

Author: William T. Trotter

Publisher: American Mathematical Soc.

Published:

Total Pages: 170

ISBN-13: 9780821871164

DOWNLOAD EBOOK

This book contains research articles and extended abstracts submitted by participants in the Planar Graphs Workshop held at DIMACS in November 1991, one of four workshops held during the DIMACS Special Year on Graph Theory and Algorithms. With more than seventy participants, the workshop drew many of the top experts in this area. The book covers a wide range of topics, including enumeration, characterization problems, algorithms, extremal problems, and network flows and geometry.


Book Synopsis Planar Graphs by : William T. Trotter

Download or read book Planar Graphs written by William T. Trotter and published by American Mathematical Soc.. This book was released on with total page 170 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains research articles and extended abstracts submitted by participants in the Planar Graphs Workshop held at DIMACS in November 1991, one of four workshops held during the DIMACS Special Year on Graph Theory and Algorithms. With more than seventy participants, the workshop drew many of the top experts in this area. The book covers a wide range of topics, including enumeration, characterization problems, algorithms, extremal problems, and network flows and geometry.

Planar Graph Drawing

Planar Graph Drawing

Author: Takao Nishizeki

Publisher: World Scientific Publishing Company

Published: 2004-09-23

Total Pages: 310

ISBN-13: 9813106409

DOWNLOAD EBOOK

The book presents the important fundamental theorems and algorithms on planar graph drawing with easy-to-understand and constructive proofs. Extensively illustrated and with exercises included at the end of each chapter, it is suitable for use in advanced undergraduate and graduate level courses on algorithms, graph theory, graph drawing, information visualization and computational geometry. The book will also serve as a useful reference source for researchers in the field of graph drawing and software developers in information visualization, VLSI design and CAD.


Book Synopsis Planar Graph Drawing by : Takao Nishizeki

Download or read book Planar Graph Drawing written by Takao Nishizeki and published by World Scientific Publishing Company. This book was released on 2004-09-23 with total page 310 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book presents the important fundamental theorems and algorithms on planar graph drawing with easy-to-understand and constructive proofs. Extensively illustrated and with exercises included at the end of each chapter, it is suitable for use in advanced undergraduate and graduate level courses on algorithms, graph theory, graph drawing, information visualization and computational geometry. The book will also serve as a useful reference source for researchers in the field of graph drawing and software developers in information visualization, VLSI design and CAD.

Math on the Move

Math on the Move

Author: Malke Rosenfeld

Publisher: Heinemann Educational Books

Published: 2016-10-18

Total Pages: 0

ISBN-13: 9780325074702

DOWNLOAD EBOOK

"Kids love to move. But how do we harness all that kinetic energy effectively for math learning? In Math on the Move, Malke Rosenfeld shows how pairing math concepts and whole body movement creates opportunities for students to make sense of math in entirely new ways. Malke shares her experience creating dynamic learning environments by: exploring the use of the body as a thinking tool, highlighting mathematical ideas that are usefully explored with a moving body, providing a range of entry points for learning to facilitate a moving math classroom. ..."--Publisher description.


Book Synopsis Math on the Move by : Malke Rosenfeld

Download or read book Math on the Move written by Malke Rosenfeld and published by Heinemann Educational Books. This book was released on 2016-10-18 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Kids love to move. But how do we harness all that kinetic energy effectively for math learning? In Math on the Move, Malke Rosenfeld shows how pairing math concepts and whole body movement creates opportunities for students to make sense of math in entirely new ways. Malke shares her experience creating dynamic learning environments by: exploring the use of the body as a thinking tool, highlighting mathematical ideas that are usefully explored with a moving body, providing a range of entry points for learning to facilitate a moving math classroom. ..."--Publisher description.

Planar Graph Drawing

Planar Graph Drawing

Author: Takao Nishizeki

Publisher: World Scientific

Published: 2004

Total Pages: 314

ISBN-13: 9789812560339

DOWNLOAD EBOOK

The book presents the important fundamental theorems and algorithms on planar graph drawing with easy-to-understand and constructive proofs. Extensively illustrated and with exercises included at the end of each chapter, it is suitable for use in advanced undergraduate and graduate level courses on algorithms, graph theory, graph drawing, information visualization and computational geometry. The book will also serve as a useful reference source for researchers in the field of graph drawing and software developers in information visualization, VLSI design and CAD.


Book Synopsis Planar Graph Drawing by : Takao Nishizeki

Download or read book Planar Graph Drawing written by Takao Nishizeki and published by World Scientific. This book was released on 2004 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book presents the important fundamental theorems and algorithms on planar graph drawing with easy-to-understand and constructive proofs. Extensively illustrated and with exercises included at the end of each chapter, it is suitable for use in advanced undergraduate and graduate level courses on algorithms, graph theory, graph drawing, information visualization and computational geometry. The book will also serve as a useful reference source for researchers in the field of graph drawing and software developers in information visualization, VLSI design and CAD.

Properties of Planar Graphs with Uniform Vertex and Face Structure

Properties of Planar Graphs with Uniform Vertex and Face Structure

Author: Joseph Malkevitch

Publisher: American Mathematical Soc.

Published: 1970

Total Pages: 124

ISBN-13: 0821812998

DOWNLOAD EBOOK


Book Synopsis Properties of Planar Graphs with Uniform Vertex and Face Structure by : Joseph Malkevitch

Download or read book Properties of Planar Graphs with Uniform Vertex and Face Structure written by Joseph Malkevitch and published by American Mathematical Soc.. This book was released on 1970 with total page 124 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Graphs on Surfaces

Graphs on Surfaces

Author: Bojan Mohar

Publisher: Johns Hopkins University Press

Published: 2001-08-02

Total Pages: 0

ISBN-13: 9780801866890

DOWNLOAD EBOOK

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.


Book Synopsis Graphs on Surfaces by : Bojan Mohar

Download or read book Graphs on Surfaces written by Bojan Mohar and published by Johns Hopkins University Press. This book was released on 2001-08-02 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.