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 Moebius 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.