Aspects of combinatorics. A wide-ranging introduction.

*(English)*Zbl 0777.05001
Cambridge: Cambridge University Press,. viii, 266 p. (1993).

This interesting book contains more than enough material for a full year undergraduate course in combinatorics. The selection is (as the author admits) a very personal one, but it represents a large variety of topics in combinatorics, ranging from the classical problems to recent development.

The text seems to be written very carefully, with a number of illustrative examples and figures. Proofs of harder results are omitted; on the other hand, in the proofs included in the book the author tries to give the reader a great deal of assistance. A nice feature is that the subjects are not grouped together but revisited many times in the course of reading.

The material is divided into 16 chapters. Each chapter is accompanied by a large selection of exercises. Most of them are provided with hints (and numerical answers) which are collected at the end of the book.

Contents: Introduction; 1. The binomial coefficients; 2. How many trees?; 3. The marriage theorem; 4. Three basic principles ( = pigeonhole, parity, inclusion-exclusion); 5. Latin squares; 6. The first theorem of graphs theory; 7. Edge-colourings; 8. Harems and tournaments; 9. Minimax theorems; 10. Recurrence; 11. Vertex-colourings; 12. Rook polynomials; 13. Planar graphs; 14. Map-colourings; 15. Designs and codes; 16. Ramsey theory; Hints for exercises; Answers to exercises; Bibliography; Index.

The text seems to be written very carefully, with a number of illustrative examples and figures. Proofs of harder results are omitted; on the other hand, in the proofs included in the book the author tries to give the reader a great deal of assistance. A nice feature is that the subjects are not grouped together but revisited many times in the course of reading.

The material is divided into 16 chapters. Each chapter is accompanied by a large selection of exercises. Most of them are provided with hints (and numerical answers) which are collected at the end of the book.

Contents: Introduction; 1. The binomial coefficients; 2. How many trees?; 3. The marriage theorem; 4. Three basic principles ( = pigeonhole, parity, inclusion-exclusion); 5. Latin squares; 6. The first theorem of graphs theory; 7. Edge-colourings; 8. Harems and tournaments; 9. Minimax theorems; 10. Recurrence; 11. Vertex-colourings; 12. Rook polynomials; 13. Planar graphs; 14. Map-colourings; 15. Designs and codes; 16. Ramsey theory; Hints for exercises; Answers to exercises; Bibliography; Index.

Reviewer: J.Širáň (Hamilton / Ontario)

##### MSC:

05-01 | Introductory exposition (textbooks, tutorial papers, etc.) pertaining to combinatorics |