four-color theorem & basic graph theory mcmullen chris [pdf]

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four-color theorem & basic graph theory mcmullen chris [pdf]

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

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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
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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).

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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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