Digraphs. Theory, algorithms and applications.

*(English)*Zbl 0958.05002
Springer Monographs in Mathematics. London: Springer. xxii, 754 p. (2001).

“Digraphs” is the first monograph to present a unified and comprehensive survey of the subject. It is divided into the following twelve major chapters: Basic terminology, notation and results. Distances. Flows in networks. Classes of digraphs. Hamiltonicity and related problems. Hamiltonian refinements. Global connectivity. Orientations of graphs. Disjoint paths and trees. Cycle structure of digraphs. Generalizations of digraphs. Additional topics.

The exercises (more than 700 altogether) at the end of each chapter with 180 figures help the reader to understand otherwise difficult concepts and proofs. Some exercises cover important or useful results not discussed in the text in detail. Many open problems and conjectures will inspire further research. The detailed subject index easily “navigates” through the whole text.

One of the main features of this book is the strong emphasis on algorithms which often play an important role in computer science, operations research, artificial intelligence, social sciences and engineering. The book may be considered as a excellent handbook on the subject for several decades to come.

The exercises (more than 700 altogether) at the end of each chapter with 180 figures help the reader to understand otherwise difficult concepts and proofs. Some exercises cover important or useful results not discussed in the text in detail. Many open problems and conjectures will inspire further research. The detailed subject index easily “navigates” through the whole text.

One of the main features of this book is the strong emphasis on algorithms which often play an important role in computer science, operations research, artificial intelligence, social sciences and engineering. The book may be considered as a excellent handbook on the subject for several decades to come.

Reviewer: Jozef Fiamčik (Prešov)