Maximal Planar Graph Theory And The Four Color Conjecture
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Maximal Planar Graph Theory And The Four Color Conjecture
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Author : Jin Xu
language : en
Publisher: Springer Nature
Release Date : 2025-05-23
Maximal Planar Graph Theory And The Four Color Conjecture written by Jin Xu and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-05-23 with Computers categories.
This open access book integrates foundational principles with advanced methodologies concerning maximal planar graphs. It offers readers an exceptional examination of graph structures, chromatic polynomials, and the construction and proof techniques of the Four-Color Conjecture. It is tailored for researchers, educators, and students involved in graph theory, combinatorics, and computational mathematics. The book consists of nine meticulously developed chapters. It starts with fundamental concepts in graph theory and then advances to pioneering computational proofs and recursive formulas of the chromatic number related to maximal planar graphs. Notable features include comprehensive discharging techniques, innovative approaches for constructing graphs of various orders, and groundbreaking conjectures concerning tree-colorability and unique four-colorability. The concluding chapter introduces Kempe's changes, offering new insights into the dynamics of graph coloring. Whether you are an academic enhancing your theoretical knowledge or a student searching for clear explanations for complex concepts, this book provides essential tools for navigating and addressing some of the most intricate challenges in graph theory. Its rigorous analysis and computational techniques equip readers with the necessary skills to engage deeply with maximal planar graph problems, making it an indispensable resource for advancing research and practical applications. No prior knowledge is necessary; however, a foundational understanding of graph theory is advised. This opportunity presents a chance to explore innovative perspectives and methodologies that expand the horizons of mathematical inquiry and proof development.
Four Colours Suffice
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Author : Robin J. Wilson
language : en
Publisher: Allan Lane
Release Date : 2002
Four Colours Suffice written by Robin J. Wilson and has been published by Allan Lane this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Mathematics categories.
A puzzlers delight for over a century, the four-colour problem was one of the most famous conundrums in mathematics, if not the most famous, and many thousands of puzzlers - amateur problem-solvers and professional mathematicians alike - have struggled to answer it. The problem is simply stated, and involves the colouring of maps: Can every map be coloured with no more than four colours so that neighbouring countries are coloured differently?
The Four Color Problem
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Author :
language : en
Publisher: Academic Press
Release Date : 2011-08-29
The Four Color Problem written by and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-08-29 with Mathematics categories.
The Four-Color Problem
The Four Color Theorem
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Author : Rudolf Fritsch
language : en
Publisher: Springer Science & Business Media
Release Date : 1998
The Four Color Theorem written by Rudolf Fritsch 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 1998 with Mathematics categories.
This elegant little book discusses a famous problem that helped to define the field now known as graph theory: what is the minimum number of colors required to print a map such that no two adjoining countries have the same color, no matter how convoluted their boundaries are. Many famous mathematicians have worked on the problem, but the proof eluded formulation until the 1970s, when it was finally cracked with a brute-force approach using a computer. The Four-Color Theorem begins by discussing the history of the problem up to the new approach given in the 1990s (by Neil Robertson, Daniel Sanders, Paul Seymour, and Robin Thomas). The book then goes into the mathematics, with a detailed discussion of how to convert the originally topological problem into a combinatorial one that is both elementary enough that anyone with a basic knowledge of geometry can follow it and also rigorous enough that a mathematician can read it with satisfaction. The authors discuss the mathematics and point to the philosophical debate that ensued when the proof was announced: just what is a mathematical proof, if it takes a computer to provide one - and is such a thing a proof at all?
The Four Color Problem
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Author : Thomas L. Saaty
language : en
Publisher:
Release Date : 1986
The Four Color Problem written by Thomas L. Saaty and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1986 with Mathematics categories.
Every Planar Map Is Four Colorable
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Author : Kenneth I. Appel
language : en
Publisher: American Mathematical Soc.
Release Date : 1989
Every Planar Map Is Four Colorable written by Kenneth I. Appel 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 1989 with Mathematics categories.
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.
Graph Theory On Demand Printing Of 02787
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Author : Frank Harary
language : en
Publisher: CRC Press
Release Date : 2018-03-05
Graph Theory On Demand Printing Of 02787 written by Frank Harary and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-03-05 with Mathematics categories.
An effort has been made to present the various topics in the theory of graphs in a logical order, to indicate the historical background, and to clarify the exposition by including figures to illustrate concepts and results. In addition, there are three appendices which provide diagrams of graphs, directed graphs, and trees. The emphasis throughout is on theorems rather than algorithms or applications, which however are occaisionally mentioned.
History Of Topology
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Author : I.M. James
language : en
Publisher: Elsevier
Release Date : 1999-08-24
History Of Topology written by I.M. James and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-08-24 with Mathematics categories.
Topology, for many years, has been one of the most exciting and influential fields of research in modern mathematics. Although its origins may be traced back several hundred years, it was Poincaré who "gave topology wings" in a classic series of articles published around the turn of the century. While the earlier history, sometimes called the prehistory, is also considered, this volume is mainly concerned with the more recent history of topology, from Poincaré onwards.As will be seen from the list of contents the articles cover a wide range of topics. Some are more technical than others, but the reader without a great deal of technical knowledge should still find most of the articles accessible. Some are written by professional historians of mathematics, others by historically-minded mathematicians, who tend to have a different viewpoint.
Pearls In Graph Theory
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Author : Nora Hartsfield
language : en
Publisher: Courier Corporation
Release Date : 2003-01-01
Pearls In Graph Theory written by Nora Hartsfield and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-01-01 with Mathematics categories.
Improved by more than a dozen new exercises, an augmented section on labeling, the simplification of many proofs, and corrections suggested by classroom users and reviewers, this delightful text on graph theory retains and strengthens the appealing features of the original edition. It is an innovative and stimulating view of mathematics designed to appeal to teachers and students alike. Pearls in Graph Theory is based on twenty years of teaching by the leading researcher in graph theory. Unlike most texts on graph theory, this book is written in an informal style suitable for students in a variety of disciplines, though mathematics majors will find the material of sufficient depth and challenge. Covering major topics and theorems in graph theory, the text provides students with a solid foundation while keeping the material enjoyably accessible and entertaining. This course typically draws 50 to 70 students per year at the University of California, San Diego. The concrete nature of the topics, as well as the broad coverage of the field, allow the book to be used for a survey course at smaller schools with no undergraduate courses in graph theory. The only requirement is some mathematical maturity, about the level attained by a successful calculus student.
Exercises In Graph Theory
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Author : O. Melnikov
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-18
Exercises In Graph Theory written by O. Melnikov 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 2013-04-18 with Mathematics categories.
This book supplements the textbook of the authors" Lectures on Graph The ory" [6] by more than thousand exercises of varying complexity. The books match each other in their contents, notations, and terminology. The authors hope that both students and lecturers will find this book helpful for mastering and verifying the understanding of the peculiarities of graphs. The exercises are grouped into eleven chapters and numerous sections accord ing to the topics of graph theory: paths, cycles, components, subgraphs, re constructibility, operations on graphs, graphs and matrices, trees, independence, matchings, coverings, connectivity, matroids, planarity, Eulerian and Hamiltonian graphs, degree sequences, colorings, digraphs, hypergraphs. Each section starts with main definitions and brief theoretical discussions. They constitute a minimal background, just a reminder, for solving the exercises. the presented facts and a more extended exposition may be found in Proofs of the mentioned textbook of the authors, as well as in many other books in graph theory. Most exercises are supplied with answers and hints. In many cases complete solutions are given. At the end of the book you may find the index of terms and the glossary of notations. The "Bibliography" list refers only to the books used by the authors during the preparation of the exercisebook. Clearly, it mentions only a fraction of available books in graph theory. The invention of the authors was also driven by numerous journal articles, which are impossible to list here.