The Ramsey number for 3-uniform tight hypergraph cycles

Combinatorics Probability and Computing

Volumn 18, Issue 1-2, 2009, Pages 165-203

  Haxell, P E ^a   Luczak T ^b   Peng, Y ^c   Rodl V ^d   Rucinski A ^b   Skokan, J ^e  

^a UNIVERSITY OF WATERLOO   (Canada)

^b ADAM MICKIEWICZ UNIVERSITY   (Poland)

^c INDIANA STATE UNIVERSITY   (United States)

^d EMORY UNIVERSITY   (United States)

^e LONDON SCHOOL OF ECONOMICS   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

HYPERGRAPH; INTEGER-N; RAMSEY NUMBERS; REGULARITY LEMMA;

GRAPH THEORY;

EID: 67649235136     PISSN: 09635483     EISSN: 14692163     Source Type: Journal    
DOI: 10.1017/S096354830800967X     Document Type: Article

References (19)

1. Bondy, J. A. and Erdos, P. (1973) Ramsey numbers for cycles in graphs. J. Combin. Theory Ser. B 14 46-54.
2. Conlon, D., Fox, J. and Sudakov, B. Ramsey numbers of sparse hypergraphs. Random Struct. Algorithms, to appear.
3. Cooley, O., Fountoulakis, N., Kühn, D. and Osthus, D. (2008) 3-uniform hypergraphs of bounded degree have linear Ramsey numbers. J. Combin. Theory Ser. B 98 484-505.
4. Cooley, O., Fountoulakis, N., Kühn, D. and Osthus, D. Embeddings and Ramsey numbers of sparse κ-uniform hypergraphs. Combinatorica, to appear.
5. Faudree, R. and Schelp, R. (1974) All Ramsey numbers for cycles in graphs. Discrete Math. 8 313-329.
6. Figaj, A. and Łuczak, T. (2007) The Ramsey number for a triple of long even cycles. J. Combin. Theory Ser. B 97 584-596.
7. Frankl, R and Rödl, V. (2002) Extremal problems on set systems. Random Struct. Algorithms 20 131-164.
8. Gyárfás, A, Sárközy, G. and Szemerédi, E. (2008) The Ramsey number of diamond-matchings and loose cycles in hypergraphs. Electron. J. Combin. 15 #R126.
9. Gyárfás, A., Sárközy, G. and Szemerédi, E. Long monochromatic Berge cycles in colored 4-uniform hypergraphs. Submitted.
10. Gyárfás, A., Sárközy, G. and Szemerédi, E. Monochromatic Hamiltonian 3-tight Berge cycles in 2-colored 4-uniform hypergraphs. Submitted.
11. Haxell, R, Łuczak, T, Peng, Y., Rödl, V., Ruciński, A., Simonovits, M. and Skokan, J. (2006) The Ramsey number for hypergraph cycles I. J. Combin. Theory Ser. A 113 67-83.
12. Haxell, P., Łuczak, T, Peng, Y., Rödl, V., Ruciński, A. and Skokan, J. (2007) The Ramsey number for hypergraph cycles II. CDAM Research Report LSE-CDAM-2007-04.
13. n) ≤ (4 + 0(l))n. J. Combin. Theory Ser. B 75 174-187.
14. Nagle, B., Olsen, S., Rödl, V. and Schacht, M. (2008) On the Ramsey number of sparse 3-graphs. Graphs Combin. 24 205-228.
15. Polcyn, J., Rödl, V., Rucinski, A. and Szemerédi, E. (2006) Short paths in quasi-random triple systems with sparse underlying graphs. J. Combin. Theory Ser. B 96 584-607.
16. Radziszowski, S. P. (1994) Small Ramsey numbers. Electronic J. Combin. 1, Dynamic Survey 1, 30 pp.
17. Rödl, V., Ruciński, A. and Szemerédi, E. (2006) A Dirac-type theorem for 3-uniform hypergraphs. Combin. Probab. Comput. 15 253-279.
18. Rosta, V. (1973) On a Ramsey-type problem of J. A. Bondy and P. Erdos, I and IL J. Combin. Theory Ser. B 15 94-104, 105-120.
19. Szemerédi, E. (1978) Regular partitions of graphs. In Problèmes Combinatoires et Théorie des Graphes (Colloq. Internat. CNRS, Univ. Orsay, Orsay, 1976), Vol. 260 of Colloq. Internat. CNRS, CNRS, Paris, pp. 399-401.