The study of directed graphs has developed enormously over recent decades, yet no book covers more than a tiny fraction of the results from more than 3000 research articles on the topic. Digraphs is the first book to present a unified and comprehensive survey of the subject. In addition to covering the theoretical aspects, including detailed proofs of many important results, the authors present a number of algorithms and applications. The applications of digraphs and their generalizations include among other things recent developments in the Travelling Salesman Problem, genetics and network connectivity. More than 700 exercises and 180 figures will help readers to study the topic while open problems and conjectures will inspire further research. This book will be essential reading and reference for all graduate students, researchers and professionals in mathematics, operational research, computer science and other areas who are interested in graph theory and its applications. Graph theory is a very popular area of discrete mathematics with not only numerous theoretical developments, but also countless applications to prac tical problems. As a research area, graph theory is still relatively young, but it is maturing rapidly with many deep results having been discovered over the last couple of decades. The theory of graphs can be roughly partitioned into two branches: the areas of undirected graphs and directed graphs (digraphs). Even though both areas have numerous important applications, for various reasons, undirected graphs have been studied much more extensively than directed graphs. One of the reasons is that undirected graphs form in a sense a special class of directed graphs (symmetric digraphs) and hence problems that can be for mulated for both directed and undirected graphs are often easier for the latter. Another reason is that, unlike for the case of undirected graphs, for which there are several important books covering both classical and recent results, no previous book covers more than a small fraction of the results obtained on digraphs within the last 25 years. Typically, digraphs are consid ered only in one chapter or by a few elementary results scattered throughout the book. Despite all this, the theory of directed graphs has developed enormously within the last three decades. There is an extensive literature on digraphs (more than 3000 papers). Many of these papers contain, not only interesting theoretical results, but also important algorithms as well as applications. Front Matter....Pages i-xxii Basic Terminology, Notation and Results....Pages 1-44 Distances....Pages 45-93 Flows in Networks....Pages 95-170 Classes of Digraphs....Pages 171-226 Hamiltonicity and Related Problems....Pages 227-280 Hamiltonian Refinements....Pages 281-343 Global Connectivity....Pages 345-414 Orientations of Graphs....Pages 415-473 Disjoint Paths and Trees....Pages 475-544 Cycle Structure of Digraphs....Pages 545-590 Generalizations of Digraphs....Pages 591-638 Additional Topics....Pages 639-682 Back Matter....Pages 683-754 Presenting a unified and comprehensive survey of directed graphs, this text covers the theoretical aspects, including detailed proofs of many important results, and also presents a number of algorithms and applications. Over 700 exercises and 180 figures are included to explain the topic.
