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The Fascinating World of Graph Theory$
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Ping Zhang, Gary Chartrand, and Arthur Benjamin

Print publication date: 2017

Print ISBN-13: 9780691175638

Published to Princeton Scholarship Online: May 2018

DOI: 10.23943/princeton/9780691175638.001.0001

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Coloring Graphs

Coloring Graphs

Chapter:
(p.206) 11 Coloring Graphs
Source:
The Fascinating World of Graph Theory
Author(s):

Arthur Benjamin

Gary Chartrand

Ping Zhang

Publisher:
Princeton University Press
DOI:10.23943/princeton/9780691175638.003.0011

This chapter considers the concept of coloring the vertices of a graph by focusing on the Four Color Problem. It begins with a discussion of three mathematics problems that involve conjecture, attributed to Pierre Fermat, Leonhard Euler, and Christian Goldbach. It then examines one of the most famous problems in mathematics, the Four Color Problem, which addresses the question of whether it is always possible to color the regions of every map with four colors so that neighboring regions are colored differently. After an overview of the origins of the Four Color Problem, the chapter goes on to analyze the Four Color Conjecture, Alfred Bray Kempe's proof of the Four Color Conjecture, and the Five Color Theorem. Finally, it looks at the Four Color Problem in the twentieth century, along with vertex colorings and their applications.

Keywords:   graph, coloring, Four Color Problem, Pierre Fermat, Leonhard Euler, Christian Goldbach, Four Color Conjecture, Alfred Bray Kempe, Five Color Theorem, vertex coloring

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