Threshold functions for asymmetric ramsey properties involving cycles

Random Structures and Algorithms

Volumn 11, Issue 3, 1997, Pages 245-276

  Kohayakawa, Y ^a   Kreuter, B ^b  

^a UNIVERSITY OF SÃO PAULO   (Brazil)

^b HUMBOLDT UNIVERSITY   (Germany)

Author keywords

Cycles; Ramsey theory; Random graphs; Szemer di's lemma; Threshold functions

Indexed keywords

EID: 0031536658     PISSN: 10429832     EISSN: None     Source Type: Journal    
DOI: 10.1002/(SICI)1098-2418(199710)11:3<245::AID-RSA3>3.0.CO;2-0     Document Type: Article

References (20)

1. B. Bollobás, Random Graphs, Academic Press, 1985.
2. S. A. Burr, A survey of noncomplete Ramsey theory for graphs, Ann. New York Acad. Sci. 328, 58-75 (1979).
3. R. L. Graham, B. Rothschild, and J. H. Spencer, Ramsey Theory, 2nd ed., Wiley-Interscience Series in Discrete Mathematics and Optimization, John Wiley & Sons, New York, 1990.
4. P. E. Haxell, Y. Kohayakawa, and T. Łuczak, The induced size-Ramsey number of cycles, Combin. Probab. Comput. 4(3), 217-239 (1995).
5. P. E. Haxell, Y. Kohayakawa, and T. Łuczak, Turán's extremal problem in random graphs: forbidding even cycles, J. Combin. Theory Ser. B 64, 273-288 (1995).
6. P. E. Haxell, Y. Kohayakawa, and T. Łuczak, Turán's extremal problem in random graphs: forbidding odd cycles, Combinatorica 16(1), 107-122 (1996).
7. S. Janson, Poisson approximation for large deviations, Random Struct. Alg. 1(2), 221-229 (1990).
8. Y. Kohayakawa, Szemerédi's regularity lemma for sparse graphs, in Foundations of Computational Mathematics, F. Cucker and M. Shub, Eds., Springer-Verlag, Berlin, 1997, pp 216-230.
9. Y. Kohayakawa, B. Kreuter, and A. Steger, An extremal problem for random graphs and the number of graphs with large even-girth, unpublished.
10. Y. Kohayakawa, T. Łuczak, and V. Rödl, Arithmetic progressions of length three in subsets of a random set, Acta Arith. LXXV(2), 133-163 (1996).
11. 4-free subgraphs of random graphs, Combinatorica, 17(2), (1997).
12. B. Kreuter, Threshold functions for asymmetric Ramsey properties with respect to vertex colorings, Random Struct. Alg. 9(3), 335-348 (1996).
13. T. Łuczak, On Ramsey minimal graphs, The Electronic Journal of Combinatorics 1:R#4 (1994).
14. T. Łuczak, A. Ruciński, and B. Voigt, Ramsey properties of random graphs, J. Combin. Theory Ser. B 56, 55-68 (1992).
15. J. Nešetřil and V. Rödl, The structure of critical Ramsey graphs, Problèmes Combinatoires et Théorie des Graphes, Colloques Internationaux CNRS 260, Univ. Orsay, Orsay, 1976, pp. 307-308.
16. J. Nešetřil and V. Rödl, The structure of critical Ramsey graphs, Acta Math. Hungar. 32(3-4), 295-300 (1978).
17. V. Rödl and A. Ruciński, Lower bounds on probability thresholds for Ramsey properties, in Combinatorics - Paul Erdos is Eighty, D. Miklós, V. T. Sós, and T. Szonyi, eds., Bolyai Society Mathematical Studies, János Bolyai Mathematical Society, Budapest, 1993, Vol. 1, pp. 317-346.
18. V. Rödl and A. Rucifiski, Random graphs with monochromatic triangles in every edge coloring, Random Struct. Alg. 5(2), 253-270 (1994).
19. V. Rödl and A. Ruciński, Threshold functions for Ramsey properties, J. Amer. Math. Soc. 8(4), 917-942 (1995).
20. E. Szemerédi, Regular partitions of graphs, Problèmes Combinatoires et Théorie des Graphes, Colloques Internationaux CNRS 260, Univ. Orsay, Orsay, 1976, pp. 399-401.