A Course in Combinatorics

Preface; 1. Graphs; 2. Trees; 3. Colorings of graphs and Ramsey's theorem; 4. Turan's theorem and extremal graphs; 5. Systems of distinct representatives; 6. Dilworth's theorem and extremal set theory; 7. Flows in networks; 8. De Bruijn sequences; 9. The addressing problem for graphs; 10. The principle of inclusion and exclusion: inversion formulae; 11. Permanents; 12. The Van der Waerden conjecture; 13. Elementary counting: Stirling numbers; 14. Recursions and generating functions; 15. Partitions; 16. (0,1)-matrices; 17. Latin squares; 18. Hadamard matrices, Reed-Muller codes; 19. Designs; 20. Codes and designs; 21. Strongly regular graphs and partial geometries; 22. Orthogonal Latin squares; 23. Projective and combinatorial geometries; 24. Gaussian numbers and q-analogues; 25. Lattices and Mobius inversion; 26. Combinatorial designs and projective geometries; 27. Difference sets and automorphisms; 28. Difference sets and the group ring; 29. Codes and symmetric designs; 30. Association schemes; 31. Algebraic graph theory: eigenvalue techniques; 32. Graphs: planarity and duality; 33. Graphs: colorings and embeddings; 34. Electrical networks and squared squares; 35. Polya theory of counting; 36. Baranyai's theorem; Appendices; Name index; Subject index.

'Both for the professional with a passing interest in combinatorics and for the students for whom it is primarily intended, this is a valuable book.' Times Higher Educational Supplement '... it will no doubt become a standard choice among the many texts on combinatorics ... fascinating ... it is highly recommended reading.' Dieter Jungnichel, Zentralblatt MATH 'This well written textbook can be highly recommended to any student of combinatorics and, because of its breadth, has many new things to tell researchers in the field also.' EMS 'This is a fascinating introduction to almost all aspects of combinatorics. Plenty of interesting problems, concrete examples, useful notes and references complement the main text. This book can be highly recommended to everyone interested in combinatorics.' Monatshefe fur Mathematik '... becoming a modern classic ... every good student should progress to this book at some stage: it is a wonderful source of elegant proofs and tantalising examples. No-one will find it easy, but every budding or established combinatorialist will be enriched by it ... This text is unashamedly and impressively mathematical; it will challenge and inform every reader and is a very significant achievement.' The Mathematical Gazette