Problems and results in extremal combinatorics - I

Discrete Mathematics

Volumn 273, Issue 1-3, 2003, Pages 31-53

  Alon, Noga ^a  

^a TEL AVIV UNIVERSITY   (Israel)

Author keywords

Extremal problems; Independent transversals; Regular subgraphs

Indexed keywords

COMPUTATIONAL GEOMETRY; MATRIX ALGEBRA; PROBLEM SOLVING; SET THEORY; THEOREM PROVING;

COMBINATORIAL GEOMETRY; DISCRETE MATHEMATICS; MATHEMATICAL INEQUALITIES;

GRAPH THEORY;

EID: 0345376932     PISSN: 0012365X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0012-365X(03)00227-9     Document Type: Conference Paper

References (46)

1. R. Aharoni, P. Haxell, Systems of disjoint representatives, preprint, 1999.
2. M. Albertson, R. Haas, A problem raised at the DIMACS Graph Coloring Week, New Jersey, 1998.
3. Alon N. The linear arboricity of graphs. Israel J. Math. 62:1988;311-325.
4. Alon N. The strong chromatic number of a graph. Random Struct. Algorithms. 3:1992;1-7.
5. Alon N., Friedland S., Kalai G. Regular subgraphs of almost regular graphs. J. Combin. Theory Ser. B. 37:1984;79-91.
6. Alon N., Kahn J., Seymour P.D. Large induced degenerate subgraphs in graphs. Graphs Combin. 3:1987;203-211.
7. Alon N., Mubayi D., Thomas R. Large induced forests in sparse graphs. J. Graph Theory. 38:2001;113-123.
8. Alon N., Pach J., Solymosi J. Ramsey-type theorems with forbidden subgraphs. Combinatorica. 21:2001;155-170.
9. Alon N., Spencer J.H. The Probabilistic Method. 2nd Edition:2000;Wiley, New York.
10. Bollobás B. Extremal Graph Theory. 1978;Academic Press, London.
11. Bollobás B. Random Graphs. 1986;Academic Press, New York.
12. Bollobás B., Erdo″s P., Strauss E.G. Complete subgraphs of chromatic graphs and hypergraphs. Utilitas Math. 6:1974;343-347.
13. Bollobás B., Erdo″s P., Szemerédi E. On complete subgraphs of. r - chromatic graphs Discrete Math. 13:1975;97-107.
14. Borsuk K. Drei Sätze über die. n -dimensionale euklidische Sphäre Fund. Math. 20:1933;177-190.
15. P. Brass, Open problem raised in the Klee-Grünbaum Festival of Geometry, April, 2000, Ein Gev, Israel.
16. Brégman L.M. Some properties of nonnegative matrices and their permanents. Soviet Math. Dokl. 14:1973;945-949. (Dokl. Akad. Nauk SSSR 211 (1973) 27-30).
17. Brégman L.M. Some properties of nonnegative matrices and their permanents. Soviet Math. Dokl. 14:1973;945-949. (Dokl. Akad. Nauk SSSR 211 (1973) 27-30).
18. Calderbank A.R., Chung F.R.K., Sturtevant D.G. Increasing sequences with nonzero block sums and increasing paths in edge ordered graphs. Discrete Math. 50:1984;15-28.
19. Chvátal V., Komlós J. Some combinatorial theorems on monotonicity. Canad. Math. Bull. 14:1971;151-157.
20. Dol'nikov V.L. Some properties of graphs of diameters. Discrete Comput. Geom. 7:2000;293-299.
21. Eggleston H.G. Covering a three-dimensional set with sets of smaller diameter. J. London Math. Soc. 30:1955;11-24.
22. Egorichev G.P. The solution of the van der Waerden problem for permanents. Dokl. Akad. Nauk SSSR. 258:1981;1041-1044.
23. Falikman D.I. A proof of Van der Waerden's conjecture on the permanent of a doubly stochastic matrix. Mat. Zametki. 29:1981;931-938.
24. S. Geschke, M. Goldstern, M. Kojman, Continuous Ramsey theory on Polish spaces and covering the plane by functions, to appear.
25. Graham R.L., Kleitman D.J. Increasing paths in edge-colored graphs. Period. Math. Hung. 3:1973;141-148.
26. Grünbaum B. A simple proof of Borsuk's conjecture in three dimensions. Proc. Cambridge Philos. Soc. 53:1957;776-778.
27. Gyárfás A. Transitive edge coloring of graphs and dimension of lattices. Combinatorica. 22:2002;479-496.
28. A. Gyárfás, M. Ruszinkó, private communication.
29. Haxell P. A note on vertex list-coloring. Combin. Probab. Comput. 10:2001;345-347.
30. Jin G. Complete subgraphs of. r -partite graphs Combin. Probab. Comput. 1:1992;241-250.
31. W.B. Johnson, J. Lindenstrauss, Extensions of Lipschitz mappings into a Hilbert space, Contemporary Mathematics, Vol. 26, AMS, Providence, RI, 1984, pp. 189-206.
32. Jukna S. Extremal Combinatorics. 2001;Springer, Berlin.
33. G.O.H. Katona, A theorem on finite sets, in: P. Erdo″s, G.O.H. Katona (Eds.), Theory of Graphs, Akadémiai Kiadó, Budapest, 1966, pp. 187-207.
34. A. Kelmans, D. Mubayi, B. Sudakov, Asymptotically optimal tree-packings in regular graphs, Electron. J. Combin. 8(R38) (2001), 8pp.
35. J.B. Kruskal, The number of simplices in a complex, in: Mathematical Optimization Techniques, Univ. California Press, Berkeley, 1963, pp. 251-278.
36. Lovász L. Combinatorial Problems and Exercises. 1979;North-Holland, Amsterdam.
37. Lovász L., Plummer M.D. Matching Theory. 1986;North-Holland, Amsterdam.
38. D. Mubayi, private communication.
39. Sachs H., Stiebitz M. Constructive methods in the theory of color-critical graphs. Discrete Math. 74:1989;201-226.
40. Schrijver A. Counting. 1 -factors in regular bipartite graphs J. Combin. Theory Ser. B. 72:1998;122-135.
41. T. Szabó, G. Tardos, Extremal problems for transversals in graphs with bounded degree, to appear.
42. J. Verstraete, private communication.
43. Vizing V.G. On an estimate on the chromatic class of a. p -graph Diskret. Analiz. 3:1964;25-30. (in Russian).
44. Wilson R.M. Decomposition of complete graphs into subgraphs isomorphic to a given graph. Congr. Numer. XV:1975;647-659.
45. Yuster R. Independent transversals in. r -partite graphs Discrete Math. 176:1997;255-261.
46. Yuster R. Large monotone paths in graphs with bounded degree. Graphs Combin. 17:2001;579-587.