Graph theory is a flourishing discipline containing a body of beautiful and powerful theorems of wide applicability. The primary aim of this book is to present a coherent introduction to the subject, suitable as a textbook for advanced undergraduate and beginning graduate students in mathematics and computer science. It provides a systematic treatment of the theory of graphs without sacrificing its intuitive and aesthetic appeal. Commonly used proof techniques are described and illustrated. A second objective is to serve as an introductionto research in graph theory. To this end, sections on more advanced topics are included, and a number of interesting and challenging open problems are highlighted and discussed in some detail. Despite this more advanced material, thebook has been organized in such a way that an introductory course on graph theory can be based on the first few sections of selected chapters. By the authors of the classic text, Graph Theory with Applications. Serves as both a textbook and an introduction to graph theory research, suitable for both mathematicians and computer scientists. Features many new exercises of varying levels ofdifficulty to help the reader master the techniques. INDICE: Graphs.- Subgraphs.- Connected Graphs.- Trees.- Separable and Nonseparable Graphs.- Tree-search Algorithms.- Flows in Networks.- Complexity of Algorithms.- Connectivity.- Planar Graphs.- The Four-Colour Problem.- Stable Sets and Cliques.- The Probabilistic Method.- Vertex Colourings.- Colourings of Maps.- Matchings.- Edge Colourings.- Hamilton Cycles.- Coverings and Packings in Directed Graphs.- Electrical Networks.- Integer Flows and Coverings.- Unresolved Problems.- References.- Index.ets with smooth boundary.- Bibliography.- Index.
- ISBN: 978-1-4419-2743-9
- Editorial: Springer
- Encuadernacion: Rústica
- Páginas: 464
- Fecha Publicación: 01/02/2009
- Nº Volúmenes: 1
- Idioma: Inglés