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.
Rezensionen / Stimmen
From the reviews:
"Digraphs (directed graphs) are a long-standing and important field of graph theory. Nevertheless, this is the first comprehensive monograph devoted to the subject. As a handbook, it addresses various groups of readers (students as well as researchers, and from various areas of applications). Throughout, because of their importance for applications, emphasis is on algorithms (in form of constructive proofs whenever possible). . a valuable and indispensable reference for many years to come. Readers and users will be thankful!" (P. Schmitt, Monatshefte für Mathematik, Vol. 141 (1), 2004)
""This is a very comprehensive volume on directed graphs and related topics. [an] impressive, well-conceived, and well-written book...it is an excellent reference.[useful] for a series of seminars, where each student would be responsible for presenting a part of the material, including proofs that are in the book and proofs that are not in the book.unlike in a large number of research monographs, the authors do an excellent job putting their topic into context. Hence the book will be useful not just for researchers focusing on digraphs, but also for everyone else for whom digraphs are tools, and not goals.
Last, but not least, an extensive list of conjectures and open questions is included in every chapter. These are typically very well presented and easy to understand. I am not taking a big risk when I predict that with the help of books like this, the area will continue to progress at a fast pace."(Miklós Bóna, MAA Online )
Sprache
Verlagsort
Verlagsgruppe
Illustrationen
1
1 s/w Abbildung
XXII, 754 p. 1 illus.
Dateigröße
ISBN-13
978-1-4471-3886-0 (9781447138860)
DOI
10.1007/978-1-4471-3886-0
Schweitzer Klassifikation
1. Basic Terminology, Notation and Results.- 2. Distances.- 3. Flows in Networks.- 4. Classes of Digraphs.- 5. Hamiltonicity and Related Problems.- 6. Hamiltonian Refinements.- 7. Global Connectivity.- 8. Orientations of Graphs.- 9. Disjoint Paths and Trees.- 10. Cycle Structure of Digraphs.- 11. Generalizations of Digraphs.- 12. Additional Topics.- References.- Symbol Index.- Author Index.
