As a complement to this series, in which the abstract theory is less important than the implications and applications of significant topics or themes, this research monograph covers of the algorithmic results attained in the area of graph connectivity, and puts emphasis on results obtained from the introduction of maximum adjacency ordering. Nagamochi (informatics, Kyoto U.) and Ibaraki (Kwansei Gakuin U.) build from the basics, starting by introducing graph theory, flows and cuts, computing connectivity, cut structures, connectivity by trees, and tree hypergraphs. They progress to maximum adjacency ordering and forest decompositions, minimum cuts, cut enumeration, cactus representations, extreme vertex sets, edge splitting, connectivity augmentation, source location problems, and semi- modular and posi-modular set function.. They include a very comprehensive bibliography. The result is a comprehensive graduate level text and a worthy addition to a professional library. Annotation ©2008 Book News, Inc., Portland, OR (booknews.com)
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 comprehensively 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.
The first really thorough book to discuss this central notion in graph and network theory, emphasising its algorithmic aspects.
