The authors of this text believe that ``after a course like this, students who subsequently attend a conference on `combinatorics' would hear no talks where they are completely lost because of unfamiliarity with the topic''. The incredible breadth of this book is indicated by the 36 chapter headings: Graphs, Trees, Colorings of graphs and Ramsey's theorem, Turan's theorem and extremal graphs, Systems of distinct representatives, Dilworth's theorem and extremal set theory, Flows in networks, De Bruijn sequences, The addressing problems for graphs, The principle of inclusion and exclusion; inversion formulae, Permanents, The van der Waerden conjecture, Elementary counting; Stirling numbers, Recursions and generating functions, Partitions, (0,1)-matrices, Latin squares, Hadamard matrices and Reed-Muller codes, Designs, Codes and designs, Strongly regular graphs and partial geometries, Orthogonal Latin squares, Projective and combinatorial geometries, Gaussian number and q-analogs, Lattices and Mobius inversion, Combinatorial designs and projective geometries, Difference sets and automorphisms, Difference sets and the group ring, Codes and symmetric designs, Association schemes, Algebraic graph theory: eigenvalue techniques, Graphs: planarity and duality, Graphs: colorings and embeddings, Electrical networks and squared squares, Polya theory of counting, and Baranyai's theorem. With such encyclopedic scope, one may well ask how it was possible to hold the book to under a thousand pages, let alone the actual 530 pages. The authors give the following clear answer in the preface: ``Of course, none of the chapters could possibly give a complete treatment of the subject indicated in their titles. Instead we cover some highlights—but we insist on doing something substantial or nontrivial with each topic.'' The reviewer believes they succeed quite well in their goal. In fact, their choice of subject matter is superb. This book would indeed make an excellent text for a full-year introduction to combinatorics. There are, however, two warnings to anyone selecting it for classroom use. First, a selection of topics must be made, as the authors point out: ``The material in every chapter has been presented in class, but we have never managed to do all the chapters in one year.'' Second, the reviewer counts a total of 214 problems, i.e. an average of fewer than 6 problems per chapter. Thus it is likely that an instructor will have to produce substantial supplementary problem sets. Apart from these minor qualifications, the reviewer believes the text is first rate.
Reviewer: Andrews, George E. [form MathSciNet]