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**About this book :- **
**The Four-Color Theorem and Basic Graph Theory**
** Chris McMullen**.

This book will take you on a tour of the four-color theorem and related concepts from graph theory. Numerous illustrations are provided to help you visualize important ideas. Concepts are explained in clear, simple terms. No prior knowledge of graph theory is assumed.

You will find in this book: what the four-color theorem is, a novel explanation for why the four-color theorem holds, the reason for working with graphs instead of maps, what triangulation is and the reason behind it, visual examples of Kempe chains and Kempe’s attempted proof, the three-edges theorem: a simplified approach to the four-color theorem, cool concepts like “quadrilateral switching” and “vertex splitting”, the distinction between planar graphs and nonplanar graphs, how to determine if a graph is a maximal planar graph or not, Euler’s formula and its relation to maximal planar graphs, explanations of Kuratowski’s theorem and Wagner’s theorem, complete graphs and complete bipartite graphs, a survey of a few named graphs such as the Fritsch and Errera graphs, how some maximal planar graphs can be trivially colored, a simple algorithm for four-coloring a maximal planar graph (Chapters 22 and 24), counting how many ways a graph can be colored using no more than four colors, comparing the coloring of a graph to a logic puzzle, Hamiltonian cycles and polygon forms of maximal planar graphs, what a separating triangle is and how to use it

May you enjoy this tour of the four-color theorem and basic graph theory.

**Book Detail :- **
** Title: ** The Four-Color Theorem and Basic Graph Theory
** Edition: **
** Author(s): ** Chris McMullen
** Publisher: ** Zishka Publishing
** Series: **
** Year: ** 2020
** Pages: ** 483
** Type: ** PDF
** Language: ** English
** ISBN: ** 1941691099,9781941691090
** Country: ** US
** Download Similar Books from Amazon**

**About Author :- **

The author ** Curtis Tracy McMullen ** is an American mathematician who is the Professor of Mathematics at
** Harvard University** . He was awarded the Fields Medal in 1998 for his work in complex dynamics, hyperbolic geometry and Teichmüller theory. McMullen graduated as valedictorian in 1980 from Williams College and obtained his Ph.D. in 1985 from Harvard University, supervised by Dennis Sullivan. He held post-doctoral positions at the
** Massachusetts Institute of Technology** , the Mathematical Sciences Research Institute, and the Institute for Advanced Study, after which he was on the faculty at
** Princeton University** (1987–1990) and the
** University of California, Berkeley ** (1990–1997), before joining Harvard in 1997.

The author, Dr. Chris McMullen, has over 20 years of experience teaching university physics in California, Oklahoma, Pennsylvania, and Louisiana (and has also taught physics to gifted high school students). Dr. McMullen currently teaches physics at Northwestern State University of Louisiana. He has also published a half-dozen papers on the collider phenomenology of superstring-inspired large extra dimensions. Chris McMullen earned his Ph.D. in particle physics from Oklahoma State University (and his M.S. in physics from California State University, Northridge).

**All Famous Books of this Author :- **

Here is list all books, text books, editions, versions or solution manuals avaliable of this author, We recomended you to download all.

** • 300+ Mathematical Pattern Puzzles, Chris McMullen **

** • Algebra Workbook Quadratic Equations, Chris McMullen **

** • Algebra Essentials Practice Workbook with Answers Linear & Quadratic Equations by Chris McMullen **

** • Systems of Equations Algebra, Chris McMullen **

** • Algebra Word Problems Practice Workbook with Full Solutions by Chris McMullen **

** • Master Essential Algebra Skills Practice Workbook with Answers by Chris McMullen **

** • Geometry Proofs Essential Practice Problems Workbook with Full Solutions by Chris McMullen **

** • The Four-Color Theorem and Basic Graph Theory by Chris McMullen **

** • The Visual Guide to Extra Dimensions Volume 1, Chris McMullen **

** • The Visual Guide to Extra Dimensions Volume 2, Chris McMullen **

** • A Visual Introduction to the Fourth Dimension, Chris McMullen **

** • Trigonometry-Essentials-Workbook--Chris-McMullen by Chris McMullen **

** • Essential Calculus-based Physics Study Guide Workbook: The Laws of Motion by Chris McMullen **

** • Essential Calculus-based Physics Study Guide Workbook: Waves, Fluids, Sound, Heat & Light by Chris McMullen **

** • A Guide to Thermal Physics by Chris McMullen **

** • Essential Modern Physics Study Guide Workbook (Full Solutions) by Chris McMullen **

** • 100 Instructive Trig-based Physics Examples Volume 2: Electricity and Magnetism by Chris McMullen **

** • Essential Trig-based Physics Study Guide Workbook: Volume 2 Electricity & Magnetism by Chris McMullen**

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**Book Contents :- **
**The Four-Color Theorem and Basic Graph Theory**
** Chris McMullen**
cover the following topics.

Introduction

1. Maps vs. Graphs

2. The Four-Color Theorem

3. Triangulation

4. Euler’s Formula

5. Complete Graphs and Bigraphs

6. Maximal Planar Graphs

7. Kempe Chains

8. A Few Notable Planar Graphs

9. Counting Ways

10. Logic Puzzle

11. Trivial Four-Coloring

12. Separating Triangles

13. Hamiltonian Cycles

14. Polygon Graphs

15. Adding Edges

16. Ultimate Four-Coloring

17. Removing Edges

18. Vertex Splitting

19. Quadrilateral Switching

20. Kirchhoff’s Rules

21. Building Blocks

22. Four-Coloring by Pairing Faces

23. The Three-Edges Theorem

24. A Recoloring Technique

25. Kempe’s Problem Revisited

26. Degrees of Separation

27. A Handwaving “Proof” of the 4CT

28. Random Notes

Answers

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