The Four-Color Theorem: History, Topological Foundations, and Idea of Proof

ISBN-13: 9781461272540 / Angielski / Miękka / 2012 / 260 str.

Rudolf Fritsch; Gerda Fritsch; J. Lie Peschke

Opis

This book discusses a famous problem that helped to define the field now known as topology: What is the minimum number of colors required to print a map so that no two adjoining countries have the same color? This problem remained unsolved until the 1950s, when it was finally cracked using a computer. This book discusses the history and mathematics of the problem, as well as the philosophical debate which ensued, regarding the validity of computer generated proofs.

Spis treści

1 History.- 2 (Topological) Maps.- 3 The Four-Color Theorem (Topological Version).- 4 Topology to Combinatorics.- 5 The Four-Color Theorem (Combinatorial Version).- 6 Reducibility.- 7 The Quest for Unavoidable Sets.- Works of Reference.