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?