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1996 | 75 | 2 | 133-163
Tytuł artykułu

Arithmetic progressions of length three in subsets of a random set

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Twórcy
  • Instituto de Matemática e Estatística, Universidade de São Paulo, Rua do Matão 1010, 05508-900 São Paulo, SP, Brazil
  • Department of Mathematics and Computer Science, Adam Mickiewicz University, Matejki 48/49, 60-769 Poznań, Poland
  • Department of Mathematics and Computer Science, Emory University, Atlanta, Georgia 30322, U.S.A.
  • Department of Mathematics and Computer Science, Emory University, Atlanta, Georgia 30322, U.S.A.
Bibliografia
  • [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.
  • [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.
  • [ET 36] P. Erdős and P. Turán, On some sequences of integers, J. London Math. Soc. 11 (1936), 261-264.
  • [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.
  • [Fu 77] H. Furstenberg, Ergodic behavior of diagonal measures and a theorem of Szemerédi on arithmetic progressions, J. Anal. Math. 31 (1977), 204-256.
  • [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.
  • [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.
  • [HKŁ 95] P. E. Haxell, Y. Kohayakawa and T. Łuczak, The induced size-Ramsey number of cycles, Combin. Probab. Comput. 4 (1995), 217-239.
  • [H-B 87] D. R. Heath-Brown, Integer sets containing no arithmetic progressions, J. London Math. Soc. 35 (1987), 385-394.
  • [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.
  • [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.
  • [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.
  • [PV 88] H.-J. Prömel and B. Voigt, A sparse Graham-Rothschild theorem, Trans. Amer. Math. Soc. 309 (1988), 113-137.
  • [Rö 90] V. Rödl, On Ramsey families of sets, Graphs Combin. 6 (1990), 187-195.
  • [Ro 53] K. F. Roth, On certain sets of integers, J. London Math. Soc. 28 (1953), 104-109.
  • [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.
  • [Sp 75] J. Spencer, Restricted Ramsey configurations, J. Combin. Theory Ser. A 19 (1975), 278-286.
  • [Sz 75] E. Szemerédi, On sets of integers containing no k elements in arithmetic progression, Acta Arith. 27 (1975), 299-345.
  • [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.
  • [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.
  • [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.
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Bibliografia
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bwmeta1.element.bwnjournal-article-aav75i2p133bwm
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