Arithmetic progressions of length three in subsets of a random set

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1. [ADLRY 94] N. Alon, R. A. Duke, H. Lefmann, V. Rödl and R. Yuster, The algorithmic aspects of the regularity lemma, J. Algorithms 16 (1994), 80-109. Zbl0794.05119
2. [EFR 86] P. Erdős, 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 (1986), 113-121. Zbl0593.05038
3. [ET 36] P. Erdős and P. Turán, On some sequences of integers, J. London Math. Soc. 11 (1936), 261-264. Zbl62.1126.01
4. [FRW 88] P. Frankl, V. Rödl and R. Wilson, The number of submatrices of a given type in a Hadamard matrix and related results, J. Combin. Theory Ser. B 44 (1988), 317-328. Zbl0658.05015
5. [Fu 77] H. Furstenberg, Ergodic behavior of diagonal measures and a theorem of Szemerédi on arithmetic progressions, J. Anal. Math. 31 (1977), 204-256. Zbl0347.28016
6. [GN 86] R. L. Graham and J. Nešetřil, Large minimal sets which force long arithmetic progressions, J. Combin. Theory Ser. A 42 (1986), 270-276. Zbl0604.05003
7. [GR 87] R. L. Graham and V. Rödl, Numbers in Ramsey theory, in: Surveys in Combinatorics 1987, C. Whitehead (ed.), London Math. Soc. Lecture Note Ser. 123, Cambridge University Press, Cambridge, 1987, 111-153. 
8. [HKŁ 95] P. E. Haxell, Y. Kohayakawa and T. Łuczak, The induced size-Ramsey number of cycles, Combin. Probab. Comput. 4 (1995), 217-239. Zbl0839.05073
9. [H-B 87] D. R. Heath-Brown, Integer sets containing no arithmetic progressions, J. London Math. Soc. 35 (1987), 385-394. Zbl0589.10062
10. [JŁR 90] S. Janson, T. Łuczak and A. Ruciński, An exponential bound for the probability of nonexistence of a specified subgraph in a random graph, in: Random Graphs '87, M. Karoński, J. Jaworski and A. Ruciński (eds.), Wiley, 1990, 73-87. Zbl0733.05073
11. [McD 89] C. J. H. McDiarmid, On the method of bounded differences, in: Surveys in Combinatorics 1989, J. Siemons (ed.), London Math. Soc. Lecture Note Ser. 141, Cambridge University Press, Cambridge, 1989, 148-188. 
12. [NR 87] J. Nešetřil and V. Rödl, Partite construction and Ramseyan theorems for sets, numbers and spaces, Comment. Math. Univ. Carolin. 28 (1987), 569-580. Zbl0629.05048
13. [PV 88] H.-J. Prömel and B. Voigt, A sparse Graham-Rothschild theorem, Trans. Amer. Math. Soc. 309 (1988), 113-137. Zbl0662.05006
14. [Rö 90] V. Rödl, On Ramsey families of sets, Graphs Combin. 6 (1990), 187-195. Zbl0705.05052
15. [Ro 53] K. F. Roth, On certain sets of integers, J. London Math. Soc. 28 (1953), 104-109. Zbl0050.04002
16. [RSz 78] I. Z. Ruzsa and E. Szemerédi, Triple systems with no six points carrying three triangles, Colloq. Math. Soc. János Bolyai 18 (1978), 939-945. Zbl0393.05031
17. [Sp 75] J. Spencer, Restricted Ramsey configurations, J. Combin. Theory Ser. A 19 (1975), 278-286. Zbl0316.05003
18. [Sz 75] E. Szemerédi, On sets of integers containing no k elements in arithmetic progression, Acta Arith. 27 (1975), 299-345. 
19. [Sz 78] E. Szemerédi, Regular partitions of graphs, in: Problèmes Combinatoires et Théorie des Graphes, Proc. Colloque Inter. CNRS, J.-C. Bermond, J.-C. Fournier, M. Las Vergnas et D. Sotteau (eds.), CNRS, Paris, 1978, 399-401. Zbl0413.05055
20. [Th 87a] A. Thomason, Pseudo-random graphs, in: Random Graphs '85, M. Karoński and Z. Palka (eds.), Ann. Discrete Math. 33, North-Holland, Amsterdam, 1987, 307-331. 
21. [Th 87b] A. Thomason, Random graphs, strongly regular graphs and pseudo-random graphs, in: Surveys in Combinatorics 1987, C. Whitehead (ed.), London Math. Soc. Lecture Note Ser. 123, Cambridge University Press, Cambridge, 1987, 173-195.