Clear, lively style covers all basics of theory and application, including mathematical models, elementary graph theory, transportation problems, connection problems, party problems, diagraphs and mathematical models, games and puzzles, more.

This volume contains the accounts of the principal survey papers presented at GRAPHS and ORDER, held at Banff, Canada from May 18 to May 31, 1984. This conference was supported by grants from the N.A.T.O. Advanced Study Institute programme, the Natural Sciences and Engineering Research Council of Canada and the University of Calgary. We are grateful for all of this considerable support. Almost fifty years ago the first Symposium on Lattice Theory was held in Charlottesville, U.S.A. On that occasion the principal lectures were delivered by G. Birkhoff, O. Ore and M.H. Stone. In those days the theory of ordered sets was thought to be a vigorous relative of group theory. Some twenty-five years ago the Symposium on Partially Ordered Sets and Lattice Theory was held in Monterey, U.S.A. Among the principal speakers at that meeting were R.P. Dilworth, B. Jonsson, A. Tarski and G. Birkhoff. Lattice theory had turned inward: it was concerned primarily with problems about lattices themselves. As a matter of fact the problems that were then posed have, by now, in many instances, been completely solved.

Continuing to provide a carefully written, thorough introduction, Graphs & Digraphs, Fifth Edition expertly describes the concepts, theorems, history, and applications of graph theory. Nearly 50 percent longer than its bestselling predecessor, this edition reorganizes the material and presents many new topics. New to the Fifth Edition New or expanded coverage of graph minors, perfect graphs, chromatic polynomials, nowhere-zero flows, flows in networks, degree sequences, toughness, list colorings, and list edge colorings New examples, figures, and applications to illustrate concepts and theorems Expanded historical discussions of well-known mathematicians and problems More than 300 new exercises, along with hints and solutions to odd-numbered exercises at the back of the book Reorganization of sections into subsections to make the material easier to read Bolded definitions of terms, making them easier to locate Despite a field that has evolved over the years, this student-friendly, classroom-tested text remains the consummate introduction to graph theory. It explores the subject’s fascinating history and presents a host of interesting problems and diverse applications.

The study of directed graphs (digraphs) has developed enormously over recent decades, yet the results are rather scattered across the journal literature. This is the first book to present a unified and comprehensive survey of the subject. In addition to covering the theoretical aspects, the authors discuss a large number of applications and their generalizations to topics such as the traveling salesman problem, project scheduling, genetics, network connectivity, and sparse matrices. Numerous exercises are included. For all graduate students, researchers and professionals interested in graph theory and its applications, this book will be essential reading.