Digraphs: Theory, Algorithms and Applications, 1st Edition
Graph theory is a very popular area of discrete mathematics with not only numerous theoretical developments, but also countless applications to practical 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 formulated 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 considered 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. This clearly indicates a real necessity for a book, covering not only the basics on digraphs, but also deeper, theoretical as well as algorithmic, results and applications.
The present book is an attempt to fill this huge gap in the literature and may be considered as a handbook on the subject. It starts at a level that can be understood by readers with only a basic knowledge in university mathematics and goes all the way up to the latest research results in several areas (including connectivity, orientations of graphs, submodular flows, paths and cycles in digraphs, generalizations of tournaments and generalizations of digraphs). The book contains more than 700 exercises and a number of applications as well as sections on highly applicable subjects. Due to the fact that we wish to address different groups of readers (advanced undergraduate and graduate students, researchers in discrete mathematics and researchers in various areas including computer science, operations research, artificial intelligence, social sciences and engineering) not all topics will be equally interesting to all potential readers. However, we strongly believe that all readers will find a number of topics of special interest to them.