# Bibliography

From Polymath Wiki

This is a (very partial) bibliography in density Ramsey theory and related topics. Additions to the bibliography are strongly encouraged!

- T. Austin, Deducing the density Hales-Jewett theorem from an infinitary removal lemma, preprint.
- H. Furstenberg, Y. Katznelson, “A density version of the Hales-Jewett theorem for
*k*= 3“, Graph Theory and Combinatorics (Cambridge, 1988). Discrete Math. 75 (1989), no. 1-3, 227–241. MR1001397 - H. Furstenberg, Y. Katznelson, “A density version of the Hales-Jewett theorem“, J. Anal. Math. 57 (1991), 64–119. MR1191743
- R. McCutcheon, “The conclusion of the proof of the density Hales-Jewett theorem for k=3“, unpublished.

- A. Hales, R. Jewett, Regularity and positional games, Trans. Amer. Math. Soc. 106 1963 222--229. MR143712
- N. Hindman, E. Tressler, "The first non-trivial Hales-Jewett number is four", preprint.
- P. Matet, "Shelah's proof of the Hales-Jewett theorem revisited", European J. Combin. 28 (2007), no. 6, 1742--1745. MR2339499
- S. Shelah, "Primitive recursive bounds for van der Waerden numbers", J. Amer. Math. Soc. 1 (1988), no. 3, 683--697. MR 929498

- E. Croot, "Szemeredi's theorem on three-term progressions, at a glance, preprint.

Behrend-type constructions

- M. Elkin, "An Improved Construction of Progression-Free Sets ", preprint.
- B. Green, J. Wolf, "A note on Elkin's improvement of Behrend's construction", preprint.
- K. O'Bryant, "Sets of integers that do not contain long arithmetic progressions", preprint.

Triangles and corners

- M. Ajtai, E. Szemerédi, Sets of lattice points that form no squares, Stud. Sci. Math. Hungar. 9 (1974), 9--11 (1975). MR369299
- I. Ruzsa, E. Szemerédi, Triple systems with no six points carrying three triangles. Combinatorics (Proc. Fifth Hungarian Colloq., Keszthely, 1976), Vol. II, pp. 939--945, Colloq. Math. Soc. János Bolyai, 18, North-Holland, Amsterdam-New York, 1978. MR519318
- J. Solymosi, A note on a question of Erdős and Graham, Combin. Probab. Comput. 13 (2004), no. 2, 263--267. MR 2047239

- P. Keevash, "Shadows and intersections: stability and new proofs", preprint.

- A. Chandra, On the solution of Moser's problem in four dimensions. Canad. Math. Bull. 16 (1973), 507--511.
- V. Chvatal, Remarks on a problem of Moser, Canadian Math Bulletin, Vol 15, 1972, 19-21.
- V. Chvatal, Edmonds polytopes and a hierarchy of combinatorial problems Discrete Math. 4 (1973) 305-337.
- Komlos, solution to problem P.170 by Leo Moser, Canad. Math.. Bull. vol (??check) (1972), 312-313, 1970.
- L. Moser, Problem P.170 in Canad. Math. Bull. 13 (1970), 268.

General texts

- R. Graham, B. Rothschild, J. Spencer, Ramsey theory, second edition, Wiley-Interscience, 1990