The Mathemathics Library created a hands-on book exhibit to celebrate the Department of Mathematics' Four Color Fest, held November 2-4, 2017. This hands-on book exhibit celebrates the mathematical, historical and cultural significance of Appel and Haken’s achievement.
Four Color Fest was held to celebrate the 40th anniversary of the proof of the Four Color Theorem and as a part of the 2017 sesquicentennial celebration of the founding of the University of Illinois.
The Four Color Theorem Exhibit was on display in the Mathematics Library October 17, 2017. For a full list of all items on display, visit A Colorful Topic: Four Color Fest.
Appel/Haken First Appel Pubication:
Display Case
Scientific American
American Mathematical Society - AMS
Every Planar Map Is Four Colorable by
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.
The Four-Color Theorem by
This little book discusses a famous problem which helped to define the field now known as topology: what is the minimum number of colours required to print a map so that no two adjoining countries have the same colour, no matter how convoluted their boundaries? Many mathematicians have worked on the problem, but the proof eluded formulation until the 1950s, when it was finally cracked with a brute-force approach using a computer. The book begins by discussing the history of the problem, and then goes into the mathematics on such a level as to allow anyone with an elementary knowledge of geometry to follow it. It is equally designed with enough rigour to keep a mathematician occupied. The authors discuss the mathematics as well as 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?
Computation of four color irreducibility by 
A Kaleidoscopic View of Graph Colorings by
This book describes kaleidoscopic topics that have developedin the area of graph colorings. Unifying current material on graph coloring,this book describes current information on vertex and edge colorings in graphtheory, including harmonious colorings, majestic colorings, kaleidoscopiccolorings and binomial colorings. Recently there have been a number of breakthroughs in vertex coloringsthat give rise to other colorings in a graph, such as graceful labelings ofgraphs that have been reconsidered under the language of colorings. The topics presented in this book include sample detailedproofs and illustrations, which depicts elements that are often overlooked.This book is ideal for graduate students and researchers in graph theory, as itcovers a broad range of topics and makes connections between recentdevelopments and well-known areas in graph theory.
Four Colors Suffice by
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.
