Graph Decompositions A Study in Infinite Graph Theory [Hardcover]

This is the first book to offer a complete account of the theory of simplicial decompositions of graphs, possibly the single most important tool in infinite graph theory. The text is centered on a number of guiding problems and concepts such as the existence and uniqueness problem of simplicial decompositions into primes, and the concept of excluded minors as a means of identifying a desired structure. Following theoretical developments since the 1930s, the author includes extensive information on the current state of research, as well as many examples, proof strategies, exercises, and ongoing problems. The book will be a useful resource for graph theorists and mathematicians, and its lively account of important research will interest advanced students as well.

1. Fundamental Facts and Concepts
2. Separating Simplices and the Existence of Prime Decompositions
3. Simplicial Minors and the Existence of Prime Decompositions
4. The Uniqueness of Prime Decompositions
5. Decompositions into Small Factors
6. Applications of Simplicial Decompositions

A textbook for an advanced course in graph theory, presenting the little known theory, simplicial decompositions of graphs, developed in the 1930s, and showing how its high degree of coherence relative to its size makes it attractive to students just embarking on their own research. --SciTech BookNews

The book offers a self-contained presentation of an interesting subject with deep results and some challenging open problems. --Choice

Presents to a broad mathematical readership the theory of simplicial decompositions of graphs, encouraging stimulation of future inquiry and research. --The New York Public Library