Revised and Updated by

Robin J. Wilson

In this revised edition, Robin Wilson has updated the terminology and notation so as to bring them in line with contemporary usage. He has added new material on interval graphs, the travelling salesman problem, bracing frameworks, shortest route problems, and coloring maps on surfaces, and has made numerous minor changes in the presentation and layout of the material, while remaining faithful to Oystein Ore's original intentions, It is his hope that a new generation of readers will thereby derive as much insight from the new edition as previous generations did in the 1960s and 1970s.

In this book Oystein Ore shows how the theory of graphs may be employed for diverse purposes such as recording a baseball league's games at every stage of the season; representing a biological breeding experiment; scheduling an efficient chess tournament; determining the cheapest way of building a railroad net; solving some ancient puzzles; analyzing winning (or losing) positions in certain games. As the reader studies these applications, he becomes increasingly interested in the properties and applications of graphs to mathematical problems. After presenting and proving Euler's formula for polyhedra, this book culminates in a discussion of the famous Four-Color Conjecture.

OYSTEIN ORE was born in Oslo, Norway, in 1899. After graduating from the University of Oslo in 1922 he continued his mathematical studies at the University of Gottingen, Germany, then as Fellow of the Mittag-Leffler Institute in Djursholm, Sweden, and received the Ph.D. in Oslo, in 1924. He spent 1925 in Paris and Gottingen as Fellow of the International Education Board, then became research associate at the University of Oslo. His career in the United States began in 1927 at Yale University where he became professor of mathematics, and where, from 1931 on, he was Sterling Professor. Oystein Ore served as chairman of Yale's mathematics department from 1939 to 1942. He was active in the American Relief Mission to Norway in the forties. In addition to over 100 mathematical research papers, Ore published a number of books, including Number Theory and its History (McGraw-Hill, 1948), Cardano, the Gambling Scholar (Princeton Press, 1953), and Niels Henrik Abel, Mathematician Extraordinary (Minnesota University Press, 1957). Oystein Ore died in 1968, in Oslo, and is buried there.


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