Dehmer M Quantitative Graph Theory Math Foundations App 2014

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?

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