Title: The Four-Color Theorem and Basic Graph Theory
Description: Explore a variety of fascinating concepts relating to the four-color theorem with an accessible introduction to related concepts from basic graph theory. From a clear explanation of Heawood’s disproof of Kempe’s argument to novel features like quadrilateral switching, this book by Chris McMullen, Ph.D., is packed with content. It even includes a novel handwaving argument explaining why the four-color theorem is true.

 - What is the four-color theorem?
 - Why is it common to work with graphs instead of maps?
 - What are Kempe chains?
 - What is the problem with Alfred Kempe’s attempted proof?
 - How does Euler’s formula relate the numbers of faces, edges, and vertices?
 - What are Kuratowski’s theorem and Wagner’s theorem?
 - What is the motivation behind triangulation?
 - What is quadrilateral switching?
 - What is vertex splitting?
 - What is the three-edges theorem?
 - Is there an algorithm for four-coloring a map or graph?
 - What is a Hamiltonian cycle?
 - What is a separating triangle?
 - How is the four-color theorem like an ill-conditioned logic puzzle?
 - Why is the four-color theorem true?
 - What makes the four-color theorem so difficult to prove by hand?
Subjects: graph theory, math, coloring