The Four-Color Theorem and Basic Graph Theory

McMullen, Chris

ISBN 10: 1941691099 / ISBN 13: 9781941691090

Editore: Zishka Publishing, 2020

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New! This book is in the same immaculate condition as when it was published 2.29.

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Dati bibliografici

• Titolo: The Four-Color Theorem and Basic Graph Theory
• Editore: Zishka Publishing
• Data di pubblicazione: 2020
• Lingua: Inglese
• ISBN 10: 1941691099
• ISBN 13: 9781941691090
• Rilegatura: Brossura
• Condizione: New

Descrizione articolo

Riassunto

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?