Preface; 1. Graphs; 2. Trees; 3. Colorings of graphs and Ramsey's theorem; 4. Turán'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 Möbius 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. Pólya theory of counting; 36. Baranyai's theorem; Appendices; Name index; Subject index.
Second edition of a popular text which covers the whole field of combinatorics.
'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.' The Times Higher Education 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 für 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
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