Publisher's Synopsis
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?
