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The last twenty years or so have seen a remarkable development in the study of finite combinatorial problems. These problems arise in a very wide variety of situations and are of pressing interest not only in the pure and applied sciences but also in fields such as sociology, economics, psychology, linguistics, games, and so on.
The theory of graphs provides a basic language and technique by means of which such problems can be isolated, analysed and exhaustively investigated. A few extensive works devoted to graph theory are now generally available, but, for the most part, these have been written with the requirements of the specialist in mind, and there has for some time been a real need for a brief introductory book written for popular consumption, without long and detailed proofs of theorems, as a whetter of the appetite and a pointer towards possible developments of the theory rather than a complete and rigorous textbook.
This little book by Professor Kaufmann, which first appeared in the French language in 1968, fulfils just such a function, and it is particularly fitting, therefore, that an English translation of it should be one of the first group of works to appear in the Transworld Student Library. The book is conceived in a manner which should appeal to the more general reader, but Professor Kaufmann is careful to give the theory a firm basis in contemporary elementary mathematics whilst at the same time stimulating the reader by frequent references to a wide variety of applications and an enticing glimpse into recent and possible future developments. In preparing and editing this translation, I have been forcibly reminded of the way in which yet another modern branch of mathematical study can provide an underlying unifying basis for a wide variety of pure and applied disciplines, The theory of graphs seems likely to be of increasing importance as the scientific study of decision-making continues its development over the next decade or so, and some familiarity with its terminology and principles is likely to be an essential part of the intellectual and practical equipment of the scientist, the sociologist, the psychologist, the economist, etc., of the immediate future