Amsterdam: Elsevier (North-Holland); Cambridge, MA: MIT Press. cii, 2198 p. Dfl. 480.00 (1995).
[The articles of this volume will be reviewed individually.]
This comprehensive handbook of combinatorics consists of two volumes divided up in five parts: Structures, Aspects, Methods, Application, and Horizons.
Volume I consists of Chapters 1 through 20: 1. Basic graph theory: Paths and circuits by J. A. Bondy, pp. 3-110; 2. Connectivity and network flows by A. Frank, 111-177; 3. Matchings and extensions by W. R. Pulleyblank, 179-232; 4. Colouring, stable sets and perfect graphs by B. Toft, 233- 288; Appendix to Chapter 4: Nowhere zero flows by P. D. Seymour, 289-299; 5. Embeddings and minors by C. Thomassen, 301-349; 6. Random graphs by M. Karoński, 351-380; 7. Hypergraphs by P. Duchet, 381-432; 8. Partially ordered sets by W. T. Trotter, 433-480; 9. Matroids: Fundamental concepts by D. J. A. Welsh, 481-526; 10. Matroid minors by P. D. Seymour, 527-550; 11. Matroid optimization and algorithms by R. E. Bixby and W. H. Cunningham, 551-609; 12. Permutation groups by P. J. Cameron, 611-645; 13. Finite geometries by P. J. Cameron, 647-691; 14. Block designs by A. E. Brouwer; 693-745; 15. Association schemes by A. E. Brouwer and W. H. Haemers, 747-771; 16. Codes by J. H. van Lint, 773-807; 17. Extremal problems in combinatorial geometry by P. Erdös and G. Purdy, 809-874; 18. Convex polytopes and related complexes by V. Klee and P. Kleinschmidt, 875-917; 19. Point lattices by J. C. Lagarias, 919-966; 20. Combinatorial number theory by C. Pomerance and A. Sárközy, 967- 1018.
Chapters 21 through 44 are found in Volume II: 21. Algebraic enumeration by I. M. Gessel and R. P. Stanley, 1021-1061; 22. Asymptotic enumeration methods by A. M. Odlyzko, 1063-1229; 23. Extremal graph theory by B. Bollobás, 1231-1292; 24. Extremal set systems by P. Frankl, 1293-1329; 25. Ramsey theory by J. Nešetřil, 1331-1403; 26. Discrepancy theory by J. Beck and V. T. Sós, 1405-1446; 27. Automorphism groups, isomorphism, reconstruction by L. Babai, 1447-1540; 28. Combinatorial optimization by M. Grötschel and L. Lovász, 1541-1597; 29. Computational complexity by D. B. Shmoys and É. Tardos, 1599-1645; 30. Polyhedral combinatorics by A. Schrijver, 1649-1704; 31. Tools from linear algebra by C. D. Godsil (with an appendix by L. Lovász), 1705- 1748; 32. Tools from higher algebra by N. Alon, 1749-1783; 33. Probabilistic methods by J. Spencer, 1785-1817; 34. Topological methods by A. Björner, 1819-1872; 35. Combinatorics in operations research by A. W. J. Kolen and J. K. Lenstra, 1875-1910; 36. Combinatorics in electrical engineering and statics by A. Recski, 1911-1924; 37. Combinatorics in statistical physics by C. D. Godsil, M. Grötschel and D. J. A. Welsh, 1925-1954; 38. Combinatorics in chemistry by D. H. Rouvray, 1955-1981; 39. Applications of combinatorics to molecular biology by M. S. Waterman, 1983-2001; 40. Combinatorics in computer science by L. Lovász, D. B. Shmoys and É. Tardos, 2003-2038; 41. Combinatorics in pure mathematics by L. Lovász, L. Pyber, D. J. A. Welsh and G. M. Ziegler, 2039-2082; 42. Infinite combinatorics by A. Hajnal, 2085-2116; 43. Combinatorial games by R. K. Guy, 2117-2162; 44. The history of combinatorics by N. L. Biggs, E. K. Lloyd and R. J. Wilson, 2163-2198.