Essentially tight bounds for rainbow cycles in proper edge-colourings

W. Rudin, Fourier analysis on groups , Wiley Classics Library, John Wiley & Sons, Inc., New York, 1990, Reprint of the 1962 original, A Wiley-Interscience Publication

1962

Earlier work this paper cites.

P. Erdős and H. Sachs, Reguläre Graphen gegebener Taillenweite mit minimaler Knotenzahl , Wiss. Z. Martin-Luther-Univ. Halle-Wittenberg Math.-Natur. Reihe 12

1963

Earlier work this paper cites.

G. A. Freĭman, On the addition of finite sets , Dokl. Akad. Nauk SSSR (1964), 1038–1041

1964

Earlier work this paper cites.

F. Jaeger, A survey of the cycle double cover conjecture , Cycles in graphs (Burnaby, B.C., 1982), North-Holland Math. Stud., vol. 115, North-Holland, Amsterdam, 1985, pp. 1–12

1985

Earlier work this paper cites.

J. Komlós and E. Szemerédi, Topological cliques in graphs II , Combinatorics, Probability and Computing 5

1996

Earlier work this paper cites.

J. Bourgain, On triples in arithmetic progression , Geom. Funct. Anal. 9

1999

Earlier work this paper cites.

S. Janson, T. Łuczak, and A. Rucinski, Random graphs , Wiley-Interscience Series in Discrete Mathematics and Optimization, Wiley-Interscience, New York, 2000

2000

Earlier work this paper cites.

N. Alon, Graph powers , Contemporary combinatorics, Bolyai Soc. Math. Stud., vol. 10, János Bolyai Math. Soc., Budapest, 2002, pp. 11–28

2002

Earlier work this paper cites.

M.-C. Chang, A polynomial bound in Freiman’s theorem , Duke Math. J. 113

2002

Earlier work this paper cites.

B. Green and I. Z. Ruzsa, Freiman’s theorem in an arbitrary abelian group , J. Lond. Math. Soc. 75

2007

Earlier work this paper cites.

P. Keevash, D. Mubayi, B. Sudakov, and J. Verstraëte, Rainbow Turán problems , Combin. Probab. Comput. 16

2007

Earlier work this paper cites.

J. Bourgain, Roth’s theorem on progressions revisited , J. Anal. Math. 104

2008

Earlier work this paper cites.

H. A. Helfgott, Growth and generation in SL 2 ​ ( ℤ / p ​ ℤ ) {\rm SL}_{2}(\mathbb{Z}/p\mathbb{Z}) , Ann. of Math. 167

2008

Earlier work this paper cites.

J. Matoušek, A. Přívětivý, and P. Škovroň, How many points can be reconstructed from k k projections? , SIAM J. Discrete Math. 22

2008

Earlier work this paper cites.

T. Tao, Product set estimates for non-commutative groups , Combinatorica 28

2008

Earlier work this paper cites.

P. Caputo, T. M. Liggett, and T. Richthammer, Proof of Aldous’ spectral gap conjecture , J. Amer. Math. Soc. 23

2010

Earlier work this paper cites.

D. Fisher, N. H. Katz, and I. Peng, Approximate multiplicative groups in nilpotent Lie groups , Proc. Amer. Math. Soc. 138

2010

Earlier work this paper cites.

T. Sanders, On a theorem of Shkredov , Online J. Anal. Comb. (2010), no. 5, 4 pp

2010

Earlier work this paper cites.

M. Bateman and N. H. Katz, Structure in additively nonsmoothing sets , preprint arXiv:1104.2862 (2011)

Original

2011

Earlier work this paper cites.

E. Breuillard, B. Green, and T. Tao, Approximate subgroups of linear groups , Geom. Funct. Anal. 21

2011

Earlier work this paper cites.

H. A. Helfgott, Growth in SL 3 ​ ( ℤ / p ​ ℤ ) {\rm SL}_{3}(\mathbb{Z}/p\mathbb{Z}) , J. Eur. Math. Soc. 13

2011

Earlier work this paper cites.

V. F. Lev and R. Yuster, On the size of dissociated bases , Electron. J. Combin. 18

2011

Earlier work this paper cites.

J. Matoušek, The number of unit distances is almost linear for most norms , Adv. Math. 226

2011

Earlier work this paper cites.

T. Sanders, On Roth’s theorem on progressions , Ann. of Math. 174

2011

Earlier work this paper cites.

I. D. Shkredov and S. Yekhanin, Sets with large additive energy and symmetric sets , J. Combin. Theory Ser. A 118

2011

Earlier work this paper cites.

S. D. Adhikari, D. J. Grynkiewicz, and Z. W. Sun, On weighted zero-sum sequences , Adv. in Appl. Math. 48

2012

Cited alongside, same era.

M. Bateman and N. H. Katz, New bounds on cap sets , J. Amer. Math. Soc. 25

2012

Cited alongside, same era.

S. Das, C. Lee, and B. Sudakov, Rainbow Turán problem for even cycles , European J. Combin. 34

2013

Cited alongside, same era.

T. Sanders, Structure in sets with logarithmic doubling , Canad. Math. Bull. 56

2013

Cited alongside, same era.

T. Sanders, The structure theory of set addition revisited , Bull. Amer. Math. Soc. 50

2013

Cited alongside, same era.

N. Gill and H. A. Helfgott, Growth in solvable subgroups of GL r ​ ( ℤ / p ​ ℤ ) {\rm GL}_{r}(\mathbb{Z}/p\mathbb{Z}) , Math. Ann. 360

J. Haslegrave, J. Hu, J. Kim, H. Liu, B. Luan, and G. Wang, Crux and long cycles in graphs , SIAM J. Discrete Math. 36

2022

Later among the works it cites.

J. Haslegrave, J. Kim, and H. Liu, Extremal density for sparse minors and subdivisions , Int. Math. Res. Not. (2022), no. 20, 15505–15548

2022

Later among the works it cites.

O. Janzer, Rainbow Turán number of even cycles, repeated patterns and blow-ups of cycles , Israel J. Math. (2022), 1–28

2022

Later among the works it cites.

P. Keevash, A. Pokrovskiy, B. Sudakov, and L. Yepremyan, New bounds for Ryser’s conjecture and related problems , Trans. Amer. Math. Soc. Ser. B 9

2022

Later among the works it cites.

A. Kupavskii, A. Polyanskii, I. Tomon, and D. Zakharov, The Extremal Number of Surfaces , Int. Math. Res. Not. (2022), no. 17, 13246–13271

2022

Later among the works it cites.