Matroid theory and its applications in electric network theory and in statics
Matroids were introduced by Whitney in 1935 as a common generalization of graphs and matrices. They received relatively little attention for about twenty years. Then in 1958 and 1959, the publication of three fundamental papers by Tutte began a period of intensive study of these structures and their properties. By 1976, the subject had grown to a state where it took Welsh over four hundred pages to provide a complete survey of the current state of knowledge in it. Continued growth since then has meant that it is no longer feasible to try to treat all of matroid theory in a single volume. The author's stated aim in this book is to give ``an introduction to matroid theory... with special emphasis on its algorithmic aspects and on the applications in electrical engineering and in statics.'' The book is in two parts. The first part (six chapters) is concerned with providing the graph-theoretic background and motivation for the study of matroids. The second part (twelve chapters) treats matroids. In each part, the odd- numbered chapters present the basic mathematical theory, while the even- numbered chapters treat associated applications. In all, about 40 \% of the material presented is on applications. This is unusual for a mathematics book so, to assist the mathematical reader, the author presents all the necessary engineering concepts. The book contains about 800 exercises and nearly 200 pages of solutions to these exercises. Moreover, there are nearly 600 figures and a bibliography of some 400 items. This book differs significantly from all the other available books on matroids in that it is aimed at engineers as well as mathematicians. It provides an interesting introduction to matroid theory. Moreover, the reader who is interested in the applications of matroids will find that this book provides the most comprehensive such treatment available.
scientific article; zbMATH DE number 193485