The Four-Color Theorem and Basic Graph Theory

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?