Publications
Preprints
Semi-algebraic colorings of complete graphs. J. Fox, J. Pach, and A. Suk.A polynomial regularity lemma for semi-algebraic hypergraphs and its applications in geometry and property testing. J. Fox, J. Pach, and A. Suk. A preliminary version appeared as:
Density and regularity theorems for semi-algebraic hypergraphs,
Proceedings of the Twenty-Sixth Annual ACM-SIAM Symposium on Discrete Algorithms, 1517-
1530, SIAM, San Diego, California, 2015.On the minimum degree of minimal Ramsey graphs for multiple
colours. J. Fox, A. Grinshpun, A. Liebenau, Y. Person, and T. Szabo.Recent developments in graph Ramsey theory. D. Conlon, J. Fox, and B.
Sudakov.Ordered Ramsey numbers. D. Conlon, J. Fox, C. Lee, and B.
Sudakov.A semi-algebraic version of Zarankiewicz's problem. J. Fox, J. Pach, A. Sheffer, A. Suk, and J. Zahl.A tight lower bound for Szemerédi's regularity lemma. J. Fox and L. M. Lovász.
To appear
Stanley-Wilf limits are typically exponential. J. Fox, Advances in Mathematics. A relative Szemerédi theorem. D. Conlon, J. Fox, and Y. Zhao, Geometric and Functional Analysis.Linear forms from the Gowers uniformity norm .
A short proof of the multidimensional Szemerédi theorem in the primes. J. Fox and Y. Zhao, American Journal of Mathematics.On the grid Ramsey problem and related questions. D. Conlon, J. Fox, C. Lee, and B.
Sudakov, International Mathematics Research Notices. A companion note can be found here.
The critical window for the classical Ramsey-Turan problem. J. Fox, P.
Loh, and Y. Zhao, Combinatorica.Ramsey numbers of cubes versus cliques. D. Conlon, J. Fox, C. Lee, and B.
Sudakov, Combinatorica.Constructing dense graphs with sublinear Hadwiger number. J. Fox, Journal of Combinatorial Theory Series B.
2015
The Erdős-Gyárfás problem on generalized Ramsey numbers. D. Conlon, J. Fox, C. Lee, and B.
Sudakov, Proceedings of the London Mathematical Society 110 (2015), 1-18.The Erdős-Hajnal conjecture for rainbow triangles. J. Fox, A. Grinshpun, and J. Pach, Journal of Combinatorial Theory Series B 111 (2015), 75-125.Easily testable graph properties. N. Alon and J. Fox, Combinatorics, Probability and Computing 24 (2015), 646-657.Distinct volume subsets. D. Conlon, J. Fox, W. Gasarch, D. G. Harris, D. Ulrich, and S. Zbarsky, SIAM Journal of Discrete Mathematics 29 (2015), 472-480.
2014
Extremal results in sparse pseudorandom graphs. D. Conlon, J. Fox, and Y. Zhao, Advances in Mathematics 256 (2014), 206-290.The Green-Tao theorem: an exposition. D. Conlon, J. Fox, and Y. Zhao, EMS Surveys in Mathematical Sciences 1 (2014), 257-291.
Ramsey-type results for semi-algebraic relations. D. Conlon, J. Fox, J. Pach, B.
Sudakov, and A. Suk, Transactions of the American Mathematical Society 366 (2014), 5043-5065. A preliminary version appeared in: Proceedings of the 29th ACM Symposium on Computational Geometry. The graph regularity method: variants, applications, and alternative methods, J. Fox, Proceedings of the International Congress of Mathematicians, Seoul, Korea, 2014, Vol. 4, 329-354.
Cycle packing. D. Conlon, J. Fox, and B. Sudakov, Random Structures and Algorithms. What is Ramsey-equivalent to a clique? J. Fox, A. Grinshpun, A. Liebenau, Y. Person, and T. Szabo, Journal of Combinatorial Theory Series B 109 (2014), 120-133.Minimum degree condition forcing complete graph immersion. M. DeVos, Z. Dvorak, J. Fox, J. McDonald, B. Mohar, and D. Scheide, Combinatorica 34 (2014), 279-298. Short proofs of some extremal results. D. Conlon, J. Fox, and B. Sudakov, Combinatorics, Probability, and Computing 23 (2014), 8-28.Applications of a new separator theorem for string graphs. J. Fox and J. Pach, Combinatorics, Probability, and Computing 23 (2014), 66-74.On grids in topological graphs. E. Ackerman, J. Fox, J. Pach, and A. Suk, Computational Geometry 47 (2014), 710-723. A preliminary version appeared in: Proceedings of the 25th ACM Symposium on Computational Geometry (2009), 403-412.
2013
Two extensions of Ramsey's theorem. D. Conlon, J. Fox, and B. Sudakov, Duke Mathematical Journal 162 (2013), 2903-2927.Chromatic number, clique subdivisions, and the conjectures of Hajos and Erdős-Fajtlowicz. J. Fox, C. Lee, and B. Sudakov, Combinatorica 33 (2013), 181-197.Graph removal lemmas. D. Conlon and J. Fox, Surveys in Combinatorics, Cambridge University Press, 2013, 1-50.Tournaments and colouring. E. Berger, K. Choromanski, M. Chudnovsky, J. Fox, M. Loebl, A. Scott, P. Seymour, and S. Thomasse, Journal of Combinatorial Theory Series B 103 (2013), 1-20.The number of edges in k-quasi-planar graphs. J. Fox, J. Pach, and A. Suk, SIAM Journal of Discrete Mathematics 27 (2013), 550-561.An improved bound for the stepping-up lemma. D. Conlon, J. Fox, and B. Sudakov, Discrete Applied Mathematics, 161 (2013), 1191-1196.A note on light geometric graphs. E. Ackerman, J. Fox, and R. Pinchasi, Discrete Mathematics, 313 (2013), 1281-1283.
2012
Bounds for graph regularity and removal lemmas. D. Conlon and J. Fox, Geometric and Functional Analysis 22 (2012), 1191-1256.Maximum union-free subfamilies. J. Fox, C. Lee, and B. Sudakov, Israel Journal of Mathematics 191 (2012), 959-971.String graphs and incomparability graphs. J. Fox and J. Pach, Advances in Mathematics 230 (2012), 1381-1401.Overlap properties of geometric expanders. J. Fox, M. Gromov, V. Lafforgue, A. Naor, and J. Pach, Journal fur die reine und angewandte Mathematik (Crelle's Journal) 671 (2012), 49-83. A preliminary version appeared in SODA 2011, 1188-1197.
Erdős-Szekeres-type theorems for monotone paths and convex bodies. J. Fox, J. Pach, B. Sudakov and A. Suk, Proceedings of the London Mathematical Society 105 (2012), 953-982.
Erratum to this paper. On a problem of Erdős and Rothschild on edges in trianges. J. Fox and P. Loh, Combinatorica 32 (2012), 619-628.On two problems in graph Ramsey theory. D. Conlon, J. Fox, and B. Sudakov, Combinatorica 32 (2012), 513-535.Erdős-Hajnal-type theorems in hypergraphs. D. Conlon, J. Fox and B. Sudakov, Journal of Combinatorial Theory Series B 102 (2012), 1142-1154.Coloring K_k-free intersection graphs of geometric objects in the plane. J. Fox and J. Pach, European Journal of Combinatorics 33 (2012), 853-866. A preliminary version appeared in Proceedings of the 24th ACM Symposium on Computational Geometry (2008), 346-354.
2011
A new proof of the graph removal lemma. J. Fox, Annals of Mathematics 174 (2011), 561-579.Large almost monochromatic subsets in hypergraphs. D. Conlon, J. Fox, and B. Sudakov, Israel Journal of Mathematics 181 (2011), 423-432.Dependent random choice. J. Fox and B. Sudakov, Random Structures and Algorithms 38 (2011), 68-99.Intersection patterns of curves. J. Fox, J. Pach, and Cs. D. Tóth, Journal of the London Mathematical Society 83 (2011), 389-406.Computing the independence number of intersection graphs. J. Fox and J. Pach, SODA 2011, 1161-1165.
2010
Hypergraph Ramsey numbers. D. Conlon, J. Fox, and B. Sudakov, Journal of the American Mathematical Society 23 (2010), 247-266.An approximate version of Sidorenko's conjecture. D. Conlon, J. Fox, and B. Sudakov, Geometric and Functional Analysis 20 (2010), 1354-1366. A short, self-contained exposition .Turán-type results for partial orders and intersection graphs of convex sets. J. Fox, J. Pach, and Cs. D. Tóth, Israel Journal of Mathematics 178 (2010), 29-50.A bipartite strengthening of the Crossing Lemma. J. Fox, J. Pach, and Cs. D. Tóth, Journal of Combinatorial Theory Series B 100 (2010) 23-35. A preliminary version appeared in the Proceedings of the 15th Symposium on Graph Drawing (Sydney, 2007), vol. 4875 of LNCS, Springer, 2008, 13-24.Complete minors and independence number. J. Fox, SIAM Journal of Discrete Mathematics 24 (2010) 1313-1321.Decompositions into subgraphs of small diameter. J. Fox and B. Sudakov, Combinatorics, Probability, and Computing 19 (2010), 753-774.A separator theorem for string graphs and its applications. J. Fox and J. Pach, Combinatorics, Probability, and Computing 19 (2010), 371-390.Directed graphs without short cycles. J. Fox, P. Keevash, and B. Sudakov, Combinatorics, Probability, and Computing 19 (2010), 285-301.Crossings between curves with many tangencies. J. Fox, F. Frati, R. Pinchasi, and J. Pach, Proceedings of WALCOM: Workshop on Algorithms and Computation, Lecture Notes in Computer Science 5942, Springer-Verlag (2010), 1-8.
2009
Density theorems for bipartite graphs and related Ramsey-type results. J. Fox and B. Sudakov, Combinatorica 29 (2009), 153-196.Ramsey numbers of sparse hypergraphs. D. Conlon, J. Fox, and B. Sudakov, Random Structures and Algorithms 35 (2009), 1-14.Large induced trees in K_r-free graphs. J. Fox, P. Loh, and B. Sudakov, Journal of Combinatorial Theory Series B 99 (2009), 494-501.Two remarks on the Burr-Erdős conjecture. J. Fox and B. Sudakov, European Journal of Combinatorics 30 (2009), 1630-1645.Paths and stability number in digraphs. J. Fox and B. Sudakov, Electronic Journal of Combinatorics 16 (2009), N23.Crossings, colorings, and cliques. M. O. Albertson, D. W. Cranston, and J. Fox, Electronic Journal of Combinatorics 16 (2009), R45.
2008
Induced Ramsey-type theorems. J. Fox and B. Sudakov, Advances in Mathematics 219 (2008), 1771-1800.Separator theorems and Turán-type results for planar intersection graphs. J. Fox and J. Pach, Advances in Mathematics 219 (2008),
1070-1080.On a problem of Duke, Erdős, and Rödl on cycle-connected subgraphs. J. Fox and B. Sudakov, Journal of Combinatorial Theory Series B 98 (2008), 1056-1062.Ramsey-type problem for an almost monochromatic K_4. J. Fox and B. Sudakov, SIAM Journal of Discrete Mathematics 23 (2008), 155-162.Erdős-Hajnal-type results on intersection patterns of geometric objects. J. Fox and J. Pach, Horizon of Combinatorics (G.O.H. Katona
et al., eds.), Bolyai Society Studies in Mathematics, Springer (2008),
79-103.Unavoidable patterns. J. Fox and B. Sudakov, Journal of Combinatorial Theory Series A 115 (2008), 1561-1569.
Undergraduate research
A Bipartite Analogue of Dilworth's Theorem for Multiple Partial Orders. J. Fox and J. Pach, European Journal of Combinatorics 30 (2009), 1846-1853. On the decay of crossing numbers.
J. Fox and Cs. D. Tóth, J. Combinatorial Theory Ser. B 98 (2008), 33-42. Also in the Proceedings of the 14th Symposium on Graph Drawing (Karlsruhe, 2006), vol. 4372 of LNCS,
Springer-Verlag, 174-183.There Exist Graphs with Super-Exponential Ramsey Multiplicity Constant.
J. Fox, Journal of Graph Theory 57 (2008), 89-98.Rainbow Solutions to the Sidon Equation. J. Fox, M. Mahdian, and R. Radoicic, Discrete Mathematics 308 (2008), 4773-4778.An infinite color analogue of Rado's theorem.
J. Fox, Journal of Combinatorial Theory Series A 114 (2007), 1456-1469.Minimal colorings without monochromatic solutions to a linear equation.
B. Alexeev, J. Fox, and R. Graham, Integers 7(2) (2007), A1.Sub-Ramsey numbers for arithmetic progressions and the Sidon equation.
J. Fox, V. Jungic, and R. Radoicic, Integers 7(2) (2007), A12.The Minimum Degree of Ramsey Minimal Graphs.
J. Fox and K. Lin, Journal of Graph Theory 54 (2007), 167-177.A Bipartite Analogue of Dilworth's Theorem.
J. Fox, Order 23 (2006), 197-209.On Rado's Boundedness Conjecture.
J. Fox and D. J. Kleitman, Journal of Combinatorial Theory Series A 113 (2006), 84-100.On the Degree of Regularity of Generalized van der Waerden Triples.
J. Fox and R. Radoicic, Integers 5 (2005), A32.Rainbow Arithmetic Progressions and Anti-Ramsey Results.
V. Jungic, J. Licht (Fox), M. Mahdian, J. Nesetril, and R. Radoicic, Combinatorics, Probability, and Computing 12 (2003), 599-620.