Algorithmic Aspects of Graph Connectivity

Algorithmic Aspects of Graph Connectivity is the first comprehensive book on this central notion in graph and network theory, emphasizing its algorithmic aspects. Because of its wide applications in the fields of communication, transportation, and production, graph connectivity has made tremendous algorithmic progress under the influence of the theory of complexity and algorithms in modern computer science. The book contains various definitions of connectivity, including edge-connectivity and vertex-connectivity, and their ramifications, as well as related topics such as flows and cuts. The authors thoroughly discuss new concepts and algorithms that allow for quicker and more efficient computing, such as maximum adjacency ordering of vertices. Covering both basic definitions and advanced topics, this book can be used as a textbook in graduate courses in mathematical sciences, such as discrete mathematics, combinatorics, and operations research, and as a reference book for specialists in discrete mathematics and its applications.

1. Introduction; 2. MA ordering and forest decompositions; 3. Minimum cuts; 4. Cut enumeration; 5. Cactus representations; 6. Extreme vertex sets; 7. Edge-splitting; 8. Connectivity augmentation; 9. Source location problems; 10. Submodular and posi-modular set functions.

With applications in communication, transportation, and production, graph connectivity has thrived using the theory of complexity and algorithms in modern computer science. This is the first thorough book on this central notion in graph and network theory, and covers new concepts and algorithms for quicker and more efficient computing.

Hiroshi Nagamochi is a professor at the Graduate School of Informatics, Kyoto University, Japan. He is a member of the Operations Research Society of Japan and the Information Processing Society.
Toshihide Ibaraki is a Professor with Kwansei Gakuin University, Japan and Professor Emeritus of Kyoto University, Japan. He is a Fellow of the ACM and Operations Research Society of Japan.