Издательство McGraw-Hill, 1997, -302 pp.The theory of graphs, with its diverse applications in natural and social sciences in general and in theoretical computer science in particular, is becoming an important component of the mathematics curriculum in colleges and universities all over the world. This book presents the basic concepts of contemporary graph theory in a sequence of nine chapters. It is primarily designed as a supplementary textbook for mathematics and computer science students with a wide range of maturity. At the same time it can also serve as a useful reference book for many academic and industrial professionals who are interested in graph theory.
Graph Theory can be considered a companion volume to Combinatorics, which was published as a Schaum Outline in 1995. The style of presentation of the material is the same in both outlines. In each chapter the basic concepts are developed in the first few pages by giving definitions and statements of the major theorems to familiarize the reader with topics that will be fully explored in the selection of solved problems that follow the text. The problems are grouped by topics and are presented in increasing order of maturity and sophistication. In some cases the results established as solutions of problems are some deep theorems and proofs of conjectures that have remained unsettled for several years.
In writing this book I have benefited enormously from the contributions of other mathematicians and scientists. My book brings together the main ideas of graph theory that I learned from the scholarly writings of others distinguished in the field, and no originality is claimed as far as the results presented in the outline are concerned. At the same time, if there are any errors, I accept complete responsibility for their occurrence, and they will be rectified in a subsequent printing of this outline once they are brought to my attention. Any feedback from the reader in this context will be gratefully acknowledged. My e-mail address is [email protected] and may be used for this purpose.
Since this outline provides basic theory and solved problems, in many cases explicit references are not made to the source of the material. Many people deserve recognition for their specific contributions, and a partial list of books that helped me to prepare this outline is appended as a Select Bibliography for further study.Graphs and Digraphs
Connectivity
Eulerian and Hamiltonian Graphs
Optimization Involving Trees
Shortest Path Problems
Flows, Connectivity, and Combinatorics
Matchings and Factors
Graph Embeddings
Colorings of Graphs
