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As American mathematicians began to take an active interest in graph theory in the last quarter of the 19th century, developments were continuing in Eu rope. In Scotland, P. G. Tait tried to simplify Kempe's proof of the four color theorem by coloring the boundary edges of a map rather than the countries. In England, Percy Heawood pointed out the flaw in Kempe's proof and investigated colorings of maps on surfaces other than the sphere. Later explorations into coloring maps on surfaces were made by Lothar Heffter of Germany, who studied orientable surfaces, and Heinrich Tietze of Austria, who investigated non-orientable ones. In Denmark, Julius Petersen discussed the factorization of graphs, while in Germany, Hermann Minkowski tried to convince his students that he could prove the four color theorem.These writers used differing terminologies when describing maps. Countries (called "districts" by Kempe and Story) were often called "regions", whereas the bound aries of a country were called "lines", "edges", or "sides", and meeting points of countries and bound aries were "points" or "vertices". We shall use these terms interchangeably, generally following the use by the person whose

Author

Robin J. Wilson, John J. Watkins, David J. Parks

Publisher

Princeton University Press

Published

2022

Language

EN

ISBN

9780691240657

Subjects

History, Mathematics, Computer Science