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The Four Color Theorem And Basic Graph Theory
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Book Synopsis The Four-Color Theorem by : Rudolf Fritsch
Download or read book The Four-Color Theorem written by Rudolf Fritsch and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 269 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book discusses a famous problem that helped to define the field now known as topology: What is the minimum number of colors required to print a map so that no two adjoining countries have the same color? This problem remained unsolved until the 1950s, when it was finally cracked using a computer. This book discusses the history and mathematics of the problem, as well as the philosophical debate which ensued, regarding the validity of computer generated proofs.
Book Synopsis The Four-Color Theorem and Basic Graph Theory by : Chris McMullen
Download or read book The Four-Color Theorem and Basic Graph Theory written by Chris McMullen and published by . This book was released on 2020-05-26 with total page 426 pages. Available in PDF, EPUB and Kindle. Book excerpt: Explore a variety of fascinating concepts relating to the four-color theorem with an accessible introduction to related concepts from basic graph theory. From a clear explanation of Heawood's disproof of Kempe's argument to novel features like quadrilateral switching, this book by Chris McMullen, Ph.D., is packed with content. It even includes a novel handwaving argument explaining why the four-color theorem is true. What is the four-color theorem? Why is it common to work with graphs instead of maps? What are Kempe chains? What is the problem with Alfred Kempe's attempted proof? How does Euler's formula relate the numbers of faces, edges, and vertices? What are Kuratowski's theorem and Wagner's theorem? What is the motivation behind triangulation? What is quadrilateral switching? What is vertex splitting? What is the three-edges theorem? Is there an algorithm for four-coloring a map or graph? What is a Hamiltonian cycle? What is a separating triangle? How is the four-color theorem like an ill-conditioned logic puzzle? Why is the four-color theorem true? What makes the four-color theorem so difficult to prove by hand?
Book Synopsis Graphs, Colourings and the Four-Colour Theorem by : Robert A. Wilson
Download or read book Graphs, Colourings and the Four-Colour Theorem written by Robert A. Wilson and published by OUP Oxford. This book was released on 2002-01-24 with total page 153 pages. Available in PDF, EPUB and Kindle. Book excerpt: The four-colour theorem is one of the famous problems of mathematics, that frustrated generations of mathematicians from its birth in 1852 to its solution (using substantial assistance from electronic computers) in 1976. The theorem asks whether four colours are sufficient to colour all conceivable maps, in such a way that countries with a common border are coloured with different colours. The book discusses various attempts to solve this problem, and some of the mathematics which developed out of these attempts. Much of this mathematics has developed a life of its own, and forms a fascinating part of the subject now known as graph theory. The book is designed to be self-contained, and develops all the graph-theoretical tools needed as it goes along. It includes all the elementary graph theory that should be included in an introduction to the subject, before concentrating on specific topics relevant to the four-colour problem. Part I covers basic graph theory, Euler's polyhedral formula, and the first published false `proof' of the four-colour theorem. Part II ranges widely through related topics, including map-colouring on surfaces with holes, the famous theorems of Kuratowski, Vizing, and Brooks, the conjectures of Hadwiger and Hajos, and much more besides. In Part III we return to the four-colour theorem, and study in detail the methods which finally cracked the problem.
Book Synopsis Four Colors Suffice by : Robin J. Wilson
Download or read book Four Colors Suffice written by Robin J. Wilson and published by Princeton University Press. This book was released on 2002 with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt: On October 23, 1852, Professor Augustus De Morgan wrote a letter to a colleague, unaware that he was launching one of the most famous mathematical conundrums in history--one that would confound thousands of puzzlers for more than a century. This is the amazing story of how the "map problem" was solved. The problem posed in the letter came from a former student: What is the least possible number of colors needed to fill in any map (real or invented) so that neighboring counties are always colored differently? This deceptively simple question was of minimal interest to cartographers, who saw little need to limit how many colors they used. But the problem set off a frenzy among professional mathematicians and amateur problem solvers, among them Lewis Carroll, an astronomer, a botanist, an obsessive golfer, the Bishop of London, a man who set his watch only once a year, a California traffic cop, and a bridegroom who spent his honeymoon coloring maps. In their pursuit of the solution, mathematicians painted maps on doughnuts and horseshoes and played with patterned soccer balls and the great rhombicuboctahedron. It would be more than one hundred years (and countless colored maps) later before the result was finally established. Even then, difficult questions remained, and the intricate solution--which involved no fewer than 1,200 hours of computer time--was greeted with as much dismay as enthusiasm. Providing a clear and elegant explanation of the problem and the proof, Robin Wilson tells how a seemingly innocuous question baffled great minds and stimulated exciting mathematics with far-flung applications. This is the entertaining story of those who failed to prove, and those who ultimately did prove, that four colors do indeed suffice to color any map.
Book Synopsis The Four-color Problem by : Thomas L. Saaty
Download or read book The Four-color Problem written by Thomas L. Saaty and published by . This book was released on 1977 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Four-Color Problem written by and published by Academic Press. This book was released on 2011-08-29 with total page 258 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Four-Color Problem
Book Synopsis Four Colors Suffice by : Robin Wilson
Download or read book Four Colors Suffice written by Robin Wilson and published by Princeton University Press. This book was released on 2013-11-10 with total page 218 pages. Available in PDF, EPUB and Kindle. Book excerpt: First published: London: Allen Lane, 2002, under title Four colours suffice.
Book Synopsis Every Planar Map is Four Colorable by : Kenneth I. Appel
Download or read book Every Planar Map is Four Colorable written by Kenneth I. Appel and published by American Mathematical Soc.. This book was released on 1989 with total page 741 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this volume, the authors present their 1972 proof of the celebrated Four Color Theorem in a detailed but self-contained exposition accessible to a general mathematical audience. An emended version of the authors' proof of the theorem, the book contains the full text of the supplements and checklists, which originally appeared on microfiche. The thiry-page introduction, intended for nonspecialists, provides some historical background of the theorem and details of the authors' proof. In addition, the authors have added an appendix which treats in much greater detail the argument for situations in which reducible configurations are immersed rather than embedded in triangulations. This result leads to a proof that four coloring can be accomplished in polynomial time.
Book Synopsis Graph Coloring Problems by : Tommy R. Jensen
Download or read book Graph Coloring Problems written by Tommy R. Jensen and published by John Wiley & Sons. This book was released on 2011-10-24 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contains a wealth of information previously scattered in research journals, conference proceedings and technical reports. Identifies more than 200 unsolved problems. Every problem is stated in a self-contained, extremely accessible format, followed by comments on its history, related results and literature. The book will stimulate research and help avoid efforts on solving already settled problems. Each chapter concludes with a comprehensive list of references which will lead readers to original sources, important contributions and other surveys.
Book Synopsis Pearls in Graph Theory by : Nora Hartsfield
Download or read book Pearls in Graph Theory written by Nora Hartsfield and published by Courier Corporation. This book was released on 2013-04-15 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: Stimulating and accessible, this undergraduate-level text covers basic graph theory, colorings of graphs, circuits and cycles, labeling graphs, drawings of graphs, measurements of closeness to planarity, graphs on surfaces, and applications and algorithms. 1994 edition.
Book Synopsis Introduction to Graph Theory by : Koh Khee Meng
Download or read book Introduction to Graph Theory written by Koh Khee Meng and published by World Scientific Publishing Company. This book was released on 2007-03-15 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: Graph theory is an area in discrete mathematics which studies configurations (called graphs) involving a set of vertices interconnected by edges. This book is intended as a general introduction to graph theory and, in particular, as a resource book for junior college students and teachers reading and teaching the subject at H3 Level in the new Singapore mathematics curriculum for junior college. The book builds on the verity that graph theory at this level is a subject that lends itself well to the development of mathematical reasoning and proof.
Book Synopsis Introduction to Graph Theory by : Richard J. Trudeau
Download or read book Introduction to Graph Theory written by Richard J. Trudeau and published by Courier Corporation. This book was released on 2013-04-15 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: Aimed at "the mathematically traumatized," this text offers nontechnical coverage of graph theory, with exercises. Discusses planar graphs, Euler's formula, Platonic graphs, coloring, the genus of a graph, Euler walks, Hamilton walks, more. 1976 edition.
Book Synopsis Graphs, Colourings, and the Four-colour Theorem by :
Download or read book Graphs, Colourings, and the Four-colour Theorem written by and published by . This book was released on 2002 with total page 141 pages. Available in PDF, EPUB and Kindle. Book excerpt: Robert Wilson discusses the four-colour theorem and some of the mathematics which developed out of attempts to solve it. He covers basic graph theory, Euler's polyhedral formula and the first published false solution of the four-colour problem.
Book Synopsis Chromatic Graph Theory by : Gary Chartrand
Download or read book Chromatic Graph Theory written by Gary Chartrand and published by CRC Press. This book was released on 2019-11-28 with total page 503 pages. Available in PDF, EPUB and Kindle. Book excerpt: With Chromatic Graph Theory, Second Edition, the authors present various fundamentals of graph theory that lie outside of graph colorings, including basic terminology and results, trees and connectivity, Eulerian and Hamiltonian graphs, matchings and factorizations, and graph embeddings. Readers will see that the authors accomplished the primary goal of this textbook, which is to introduce graph theory with a coloring theme and to look at graph colorings in various ways. The textbook also covers vertex colorings and bounds for the chromatic number, vertex colorings of graphs embedded on surfaces, and a variety of restricted vertex colorings. The authors also describe edge colorings, monochromatic and rainbow edge colorings, complete vertex colorings, several distinguishing vertex and edge colorings. Features of the Second Edition: The book can be used for a first course in graph theory as well as a graduate course The primary topic in the book is graph coloring The book begins with an introduction to graph theory so assumes no previous course The authors are the most widely-published team on graph theory Many new examples and exercises enhance the new edition
Book Synopsis A Textbook of Graph Theory by : R. Balakrishnan
Download or read book A Textbook of Graph Theory written by R. Balakrishnan and published by Springer Science & Business Media. This book was released on 2012-09-20 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: In its second edition, expanded with new chapters on domination in graphs and on the spectral properties of graphs, this book offers a solid background in the basics of graph theory. Introduces such topics as Dirac's theorem on k-connected graphs and more.
Book Synopsis Chromatic Graph Theory by : Gary Chartrand
Download or read book Chromatic Graph Theory written by Gary Chartrand and published by CRC Press. This book was released on 2019-11-28 with total page 450 pages. Available in PDF, EPUB and Kindle. Book excerpt: With Chromatic Graph Theory, Second Edition, the authors present various fundamentals of graph theory that lie outside of graph colorings, including basic terminology and results, trees and connectivity, Eulerian and Hamiltonian graphs, matchings and factorizations, and graph embeddings. Readers will see that the authors accomplished the primary goal of this textbook, which is to introduce graph theory with a coloring theme and to look at graph colorings in various ways. The textbook also covers vertex colorings and bounds for the chromatic number, vertex colorings of graphs embedded on surfaces, and a variety of restricted vertex colorings. The authors also describe edge colorings, monochromatic and rainbow edge colorings, complete vertex colorings, several distinguishing vertex and edge colorings. Features of the Second Edition: The book can be used for a first course in graph theory as well as a graduate course The primary topic in the book is graph coloring The book begins with an introduction to graph theory so assumes no previous course The authors are the most widely-published team on graph theory Many new examples and exercises enhance the new edition
