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	标题:	A First Course in Graph Theory
	作者:	Jun-Ming Xu (徐俊明)
	出版社:	Academic Press, Beijing (科学出版社)
	书号:	ISBN 978-7-03-043863-8          页数:  457+10
	出版日期:	2015.03	字数：430千字	装帧：精装
	书价:	158:00
	邮购:	科学出版社 亚马逊 京东 当当网

 Graphs are mathematical structures used to model pairwise relations between objects. The richness of theory and the wideness of applications of graphs make it impossible to include all topics on
graphs in a book. All materials presented in this book, I think, are the most classical, fundamental, interesting and important, and some of which are new. The method dealt with the materials is to
particularly lay stress on digraphs, regarding undirected graphs as their special cases. My own experience from teaching out of the subject more than twenty years at University of Science and Technology of China (USTC) shows that this treatment makes hardly the course difficult, but much more accords with the essence and the development trend of the subject.

The book consists of eight chapters. The first two chapters introduce the most basic concepts and related results. From the third chapter to the eighth chapter, each chapter focuses on a special topic, including trees and graphic spaces, plane and planar graphs, flows and connectivity, matchings and independent sets, colorings and integer flows, graphs and groups. These topics are treated in some depth, both theoretical and applied, with some suggestions for further reading. Every effort will be made to
strengthen the mutual connections among these topics, with an aim to make the materials more systematic and cohesive. All theorems will be clearly stated, together with full and concise proofs, some of them are new. A number of examples and figures are given to help the reader to understand the given materials. To explore the mathematical nature and perfection of graph theory better, this book will specially stress the equivalence of some classical results, such as the max-flow min-cut theorem of Ford and Fulkerson, Menger's theorem, Hall's theorem, Tutte's theorem and K\"onig's theorem.

To expand the reader's scope of knowledge, some further reading materials, including self-contained proofs of some theorems, new concepts, problems and conjectures, are added to the back of some sections, separated by the stars *, at the first reading some readers may wish to skip them.

Throughout this book the reader will see that graph theory has closed connection with other branches of mathematics, including linear algebra, matrix theory, group theory, combinatorics, combinatorial optimization and operation research, and wide applications to other subjects, including computer science,
electronics, scientific management and so on. Thus, the reader who will read this book is supposed to familiarize himself with some basic concepts and methods of linear algebra and group theory. The
applications carefully selected are arranged in the latter sections of the chapter with some classical and fundamental algorithms. The aim of such arrangements is to conveniently choose these materials for some readers according to their interesting and available periods.

Exercises of each section, from routine practice to challenging, are supplements to the text. Some of them are very important results in graph theory. It is advisable for the reader to be familiar with the new definitions introduced in the exercises since they are useful for further study. The reader is also advised to do the exercises as many as he (or she) can. The harder ones are indicated by bold type.

Graph theory has experienced more than 270 years of development, many people found many important results. With the loss of time, many of the findings are gradually being forgotten. So to be able to verify the accuracy and provenance of results is vital. To this end, the book lists related references and provides brief biographical notes on major scholars mentioned in this book.