An Algorithmic Version of the Blow-Up Lemma

Random Structures and Algorithms

Volumn 12, Issue 3, 1998, Pages 297-312

  Komlós, János ^a   Sarkozy, Gabor N ^b   Szemerédi, Endre ^a  

^a RUTGERS UNIVERSITY   (United States)

^b Worcester Polytechnic Institute   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0032373312     PISSN: 10429832     EISSN: None     Source Type: Journal    
DOI: 10.1002/(SICI)1098-2418(199805)12:3<297::AID-RSA5>3.0.CO;2-Q     Document Type: Article

References (42)

1. N. Alon, Non-constructive proofs in combinatorics, Proceedings of the International Congress of Mathematics, Kyoto 1990, Japan, Springer-Verlag, Tokyo, 1991, pp. 1421-1429.
2. N, Alon, A parallel algorithmic version of the local lemma, Random Struct. Algorithms, 2, 367-378 (1991), Proceedings of the Thirty-Second IEEE FOCS (1991), pp. 586-593.
3. N, Alon, A parallel algorithmic version of the local lemma, Random Struct. Algorithms, 2, 367-378 (1991), Proceedings of the Thirty-Second IEEE FOCS (1991), pp. 586-593.
4. N. Alon, R. Duke, H. Lefman, V. Rödl, and R. Yuster, The algorithmic aspects of the regularity lemma, Proceedings of the Thirty-Third IEEE FOCS (1993), pp. 479-481, J. Algorithms, 16, 80-109 (1994).
5. N. Alon, R. Duke, H. Lefman, V. Rödl, and R. Yuster, The algorithmic aspects of the regularity lemma, Proceedings of the Thirty-Third IEEE FOCS (1993), pp. 479-481, J. Algorithms, 16, 80-109 (1994).
6. N. Alon, L. Babai, and A. Itai, A fast randomized parallel algorithm for the maximal independent set problem, J. Algorithms, 7, 567-583 (1986).
7. N. Alon and R. Yuster, Almost H-factors in dense graphs, Graphs Combin., 8, 95-102 (1992).
8. N. Alon and R. Yuster, H-factors in dense graphs, J. Combin. Theory Ser. B, 66, 269-282 (1996).
9. J. Beck, An algorithmic approach to the Lovász local lemma, Random Struct. Algorithms, 2, 343-365 (1991).
10. B. Bollobás, P. Erdös, M. Simonovits, and E. Szemerédi, Extremal graphs without large forbidden subgraphs, in Advances in Graph Theory, Cambridge Combinatorial Conference, Trinity College, 1977, Ann. Discrete Math., 3, 29-41 (1978).
11. V. Chvátal, V. Rödl, E. Szemerédi, and W. T. Trotter Jr., The Ramsey number of a graph with bounded maximum degree, J. Combin. Theory Ser. B, 34, 239-243 (1983).
12. S. A. Cook, Taxonomy of problems with fast parallel algorithms, Inform. and Control. 64, 2-22 (1985).
13. P. Erdös, P. Frankl, and V. Rödl, The asymptotic number of graphs not containing a fixed subgraph and a problem for hypergraphs having no exponent, Graphs Combin., 2, 113-121 (1986).
14. P. Franek and V. Rödl, On Erdös conjecture for multiplicities of complete subgraphs, Graphs Combin., to appear.
15. P. Frankl, R. L. Graham, and V. Rödl, On subsets of Abelian groups with no 3-term arithmetic progression, J. Combin. Theory Ser. A, 15, 157-161 (1987).
16. P. Frankl and Z. Füredi, Exact solution of some Turán-type problems, J. Combin. Theory Ser. A, 45, 226-262 (1987).
17. Z. Füredi, The maximum number of edges in a minimal graph of diameter 2, J. Graph Theory, 16, 81-98 (1992).
18. Z. Füredi, M. Goemans, and D. J. Kleitman, On the maximum number of triangles in wheel-free graphs, to appear.
19. M. Goldberg and T. Spencer, A new parallel algorithm for the maximal independent set problem, SIAM J. Comput., 18, 419-427 (1989).
20. M. Goldberg and T. Spencer, Constructing a maximal independent set in parallel, SIAM J. Disc. Math., 2, 322-328 (1989).
21. A. Hajnal, W. Maass, and G. Turán, On the communication complexity of graph properties, Proceedings of the Twentieth Symposium on Theory of Computing, 1988, pp. 186-191.
22. 5/2 algorithm for maximum matchings in bipartite graphs, SIAM J. Comput., 2, 225-231 (1973).
23. R. Karp and V. Ramachandran, Parallel algorithms for shared memory machines, in Handbook of Theoretical Computer Science, J. Van Leeuven, Ed., North-Holland, Amsterdam, 1990, pp. 869-941.
24. R. Karp and A. Wigderson, A fast parallel algorithm for the maximal independent set problem, J. Assoc. Comput. Mach., 32, 762-773 (1985).
25. J. Komlós, G. N. Sárközy, and E. Szemerédi, Proof of a packing conjecture of Bollobás Combinatorics, Probab. Comput., 4, 241-255 (1995).
26. J. Komlós, G. N. Sárközy, and E. Szemerédi, Blow-up lemma, Combinatorica, 17, 109-123 (1997).
27. J. Komlós, G. N. Sárközy, and E. Szemerédi, On the Posa-Seymour conjecture, J. Graph Theory, to appear.
28. J. Komlós, G. N. Sárközy, and E. Szemerédi, On the square of a Hamiltonian cycle in dense graphs, Random Structures and Algorithms, 9, 193-211 (1996).
29. J. Komlós, G. N. Sárközy, and E. Szemerédi, Proof of the Seymour conjecture for large graphs, submitted for publication.
30. J. Komlós, G. N. Sárközy, and E. Szemerédi, Proof of the Alon-Yuster conjecture, in preparation.
31. J. Komlós and M. Simonovits, Szemerédi's regularity lemma and its applications in graph theory, in Paul Erdös is 80, Vol. 2., Proc. Colloq. Math. Soc. János Bolyai 295-352 (1996).
32. L. Lovász and M. D. Plummer, Matching theory, Ann. Discrete Math., 29 (1986).
33. M. Luby, A simple parallel algorithm for the maximal independent set problem, SIAM J. Comput., 15, 1036-1053 (1986).
34. C. H. Papadimitriou, On graph theoretic lemmata and complexity classes, Proceedings of the Thirty-First IEEE FOCS, 1990, pp. 794-801.
35. C. H. Papadimitriou, On the complexity of the parity argument and other inefficient proofs of existence, J. Comput. System Sci., 47 (1993).
36. N. J. Pippenger, On simultaneous resource bounds, Proceedings of the Twentieth IEEE FOCS, 1979, pp. 307-311.
37. V. Rödl, On universality of graphs with uniformly distributed edges, Discrete Math., 59, 125-134 (1986).
38. G. N. Sárközy, Fast parallel algorithms for finding Hamiltonian cycles and trees in graphs, Technical Report 93-81, DIMACS, Rutgers University, New Brunswick, NJ, 1993.
39. M. Simonovits and V. T. Sös, Szemerédi's partition and quasirandomness, Random Struct. Algorithms, 2, 1-10 (1991).
40. E. Szemerédi, Regular partitions of graphs, in Colloques Internationaux C.N.R.S., J.-C. Bermond, J.-C. Fournier, M. Las Vergnas, and D. Sotteau, Eds., 1978, pp. 399-401.
41. E. Szemerédi, On a set containing no k elements in arithmetic progression, Acta Arith., XXVII, 199-245 (1975).
42. L. G. Valiant, Parallel computation, Proceedings of the Seventh IBM Symposium on Mathematical Foundations of Computer Science, 1982.