Graph Decompositions
A Study in Infinite Graph Theory
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Product details:
- Publisher Clarendon Press
- Date of Publication 13 September 1990
- ISBN 9780198532101
- Binding Hardback
- No. of pages242 pages
- Size 242x163x19 mm
- Weight 532 g
- Language English
- Illustrations numerous line illustrations 0
Categories
Short description:
Graph Decompositions is the first ever book on a topic that belongs to infinite graph theory. It offers a complete account of the theory of simplicial decompositions of graphs, from its origins in the 1930s right up to the frontiers of present-day research.
The text gives an authentic picture of research in progress. It includes discussions of examples, proof strategies, or the formation of new concepts, as well as numerous exercises and open problems.
Long description:
Graph Decompositions is the first book on a topic that belongs mainly to infinite graph theory. It offers a complete account of the theory of simplicial decompositions of graphs, from its origins in the 1930s right up to present-day research.
In addition to being one of the most important tools in infinite graph theory, simplicial decompositions may be seen as a model for any kind of structural graph decomposition. The currently topical tree-decompositions, for example, have their origin in simplicial decompositions.
The text is centred around a few guiding problems and concepts, such as the existence and the uniqueness problem of simplicial decompositions into primes, or the concept of excluded minors as a means of identifying a desired structure.It attempts to give as authentic a picture as possible of research in progress. To this end, it includes discussions of examples, proof strategies on the formation of new concepts, as well as numerous exercises and open problems.
Graph Decompositions should prove attractive to any graph theorist or other mathematician interested in a new area of research, as well as to the advanced student looking for a lively and inspiring account of how such research evolves.
'The book is undoubtedly a valuable addition to the literature of infinite graph theory' London Mathematical Society
Table of Contents:
Note to the reader; Introduction; Fundamental facts and concepts; Separating simplices and the existence of prime decompositions; Simplicial minors and the existence of prime decompositions; The uniqueness of prime decompositions; Decompositions into small factors; Applications of simplicial decompositions; Appendix: Some notes on set theory; References; Subject index; Index of symbols.
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