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Handbook of combinatorics. Vol. 1-2. (English) Zbl 0833.05001
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. Indexed articles: {\it Bondy, J.A.}, Basic graph theory: Paths and circuits, 3-110 [Zbl 0849.05044] {\it Frank, András}, Connectivity and network flows, 111-177 [Zbl 0846.05055] {\it Pulleyblank, W.R.}, Matchings and extensions, 179-232 [Zbl 0866.05048] {\it Toft, Bjarne}, Colouring, stable sets and perfect graphs, 233-288 [Zbl 0844.05042] {\it Seymour, P.D.}, Nowhere-zero flows, 289-299 [Zbl 0845.05035] {\it Thomassen, Carsten}, Embeddings and minors, 301-349 [Zbl 0851.05043] {\it Karoński, Michał}, Random graphs, 351-380 [Zbl 0845.05082] {\it Duchet, Pierre}, Hypergraphs, 381-432 [Zbl 0859.05063] {\it Trotter, William T.}, Partially ordered sets, 433-480 [Zbl 0841.06001] {\it Welsh, D.J.A.}, Matroids: Fundamental concepts, 481-526 [Zbl 0853.05023] {\it Seymour, P.D.}, Matroid minors, 527-550 [Zbl 0853.05024] {\it Bixby, Robert E.; Cunningham, William H.}, Matroid optimization and algorithms, 551-609 [Zbl 0848.05017] {\it Cameron, Peter J.}, Permutation groups, 611-645 [Zbl 0845.20001] {\it Cameron, Peter J.}, Finite geometries, 647-691 [Zbl 0854.51003] {\it Brouwer, Andries E.}, Block designs, 693-745 [Zbl 0848.05008] {\it Brouwer, Andries E.; Haemers, Willem H.}, Association schemes, 747-771 [Zbl 0849.05072] {\it van Lint, J.H.}, Codes, 773-807 [Zbl 0849.94018] {\it Erdős, Paul; Purdy, George}, Extremal problems in combinatorial geometry, 809-874 [Zbl 0852.52009] {\it Klee, Victor; Kleinschmidt, Peter}, Convex polytopes and related complexes, 875-917 [Zbl 0847.52009] {\it Lagarias, Jeffrey C.}, Point lattices, 919-966 [Zbl 0854.90116] {\it Pomerance, Carl; Sárközy, András}, Combinatorial number theory, 967-1018 [Zbl 0849.11001] {\it Gessel, Ira M.; Stanley, Richard P.}, Algebraic enumeration, 1021-1061 [Zbl 0853.05002] {\it Odlyzko, A.M.}, Asymptotic enumeration methods, 1063-1229 [Zbl 0845.05005] {\it Bollobás, Béla}, Extremal graph theory, 1231-1292 [Zbl 0844.05054] {\it Frankl, P.}, Extremal set systems, 1293-1329 [Zbl 0844.05094] {\it Nešetřil, Jaroslav}, Ramsey theory, 1331-1403 [Zbl 0848.05065] {\it Beck, József; Sós, Vera T.}, Discrepancy theory, 1405-1446 [Zbl 0851.11043] {\it Babai, László}, Automorphism groups, isomorphism, reconstruction, 1447-1540 [Zbl 0846.05042] {\it Grötschel, Martin; Lovász, László}, Combinatorial optimization, 1541-1597 [Zbl 0854.90117] {\it Shmoys, D.B.; Tardos, É.}, Computational complexity, 1599-1645 [Zbl 0844.68046] {\it Schrijver, Alexander}, Polyhedral combinatorics, 1649-1704 [Zbl 0845.90103] {\it Godsil, C.D.; Lovász, László}, Tools from linear algebra, 1705-1748 [Zbl 0859.05079] {\it Alon, Noga}, Tools from higher algebra, 1749-1783 [Zbl 0848.05073] {\it Spencer, Joel}, Probabilistic methods, 1785-1817 [Zbl 0853.60004] {\it Björner, Anders}, Topological methods, 1819-1872 [Zbl 0851.52016] {\it Kolen, Antoon W.J.; Lenstra, Jan Karel}, Combinatorics in operations research, 1875-1910 [Zbl 0854.90118] {\it Recski, András}, Combinatorics in electrical engineering and statics, 1911-1924 [Zbl 0916.05066] {\it Godsil, C.D.; Grötschel, M.; Welsh, D.J.A.}, Combinatorics in statistical physics, 1925-1954 [Zbl 0882.05014] {\it Rouvray, Dennis H.}, Combinatorics in chemistry, 1955-1981 [Zbl 0843.92027] {\it Waterman, Michael S.}, Applications of combinatorics to molecular biology, 1983-2001 [Zbl 0842.92011] {\it Lovász, László; Shmoys, D.B.; Tardos, É.}, Combinatorics in computer science, 2003-2038 [Zbl 0844.68088] {\it Lovász, László; Pyber, L.; Welsh, D.J.A.; Ziegler, G.M.}, Combinatorics in pure mathematics, 2039-2082 [Zbl 0851.52017] {\it Hajnal, A.}, Infinite combinatorics, 2085-2116 [Zbl 0844.03026] {\it Guy, Richard K.}, Combinatorial games, 2117-2162 [Zbl 0845.90145] {\it Biggs, Norman L.; Lloyd, E.Keith; Wilson, Robin J.}, The history of combinatorics, 2163-2198 [Zbl 0847.05001]

MSC:
05-06Proceedings of conferences (combinatorics)
00B15Collections of articles of miscellaneous specific interest