## Submitted

1. A. Kupavskii, Structure and properties of large intersecting families, preprint
2. F. Ihringer, A. Kupavskii, Regular intersecting families, submitted
3. A. Kupavskii, Diversity of uniform intersecting families, submitted
4. A. Kupavskii, E. Welzl, Lower bounds for searching robots, some faulty, preprint
5. M. Czikos, A. Kupavskii, N. Mustafa, The VC-dimension of Unions: Learning, Geometry and Combinatorics, submitted
6. A. Kupavskii, N. Mustafa, K. Swanepoel, Bounding the size of an almost-equidistant set in Euclidean space, submitted
7. P. Frankl, A. Kupavskii, Partition-free families of sets, submitted
8. N. Frankl, A. Kupavskii, K. Swanepoel, Unit distance representations, in preparation
9. A. Kupavskii, Random Kneser graphs and hypergraphs, submitted
10. A. Kupavskii, M. Zhukovskii, Short monadic second order sentences about sparse random graphs, submitted
11. P. Frankl, A. Kupavskii, Two problems of P. Erdős on matchings in set families, submitted
12. P. Frankl, A. Kupavskii, Families of sets with no matching of sizes 3 and 4, submitted
13. A. Kupavskii, J. Pach, G. Tardos, Controlling Lipschitz functions, submitted
14. P. Frankl, A. Kupavskii,  Erdős-Ko-Rado theorem for $\{0,\pm 1\}$-vectors, submitted

## Journal Publications

1. A. Kupavskii, D. Zakharov, Regular bipartite graphs and intersecting families, accepted at J. Comb. Th. Ser. A
2. A. Kupavskii, J. Pach, I. Tomon, On the size of $k$-cross-free families, to appear in Combinatorica
3. P. Frankl, A. Kupavskii, Families of vectors without antipodal pairs, to appear in Studia Sci. Math. Hungarica
4. P. Frankl, A. Kupavskii, Counting intersecting and pairs of cross-intersecting families, to appear in Combinatorics, Probability, and Computing
5. P. Frankl, A. Kupavskii,  Families with no s pairwise disjoint sets, Journal of the London Mathematical Society 95 (2017), N3, 875-894.
6. P. Frankl, A. Kupavskii, Intersection theorems for $\{0,\pm 1\}$-vectors and $s$-cross-intersecting families, Moscow Journal of Combinatorics and Number Theory 7 (2017), N2, 91-109.
7. P. Frankl, A. Kupavskii, A size-sensitive inequality for cross-intersecting families, European Journal of Combinatorics 62 (2017), 263-271
8. P. Frankl, A. Kupavskii,  Uniform 𝑠-cross-intersecting families, Combinatorics, Probability and Computing 26 (2017), N4, 517-524.
9. A. Kupavskii, J. Pach, From Tarski's plank problem to simultaneous approximation, The American Math. Monthly 124 (2017), N6, 494-505.
10. A. Kupavskii, A. Polyanskii, Proof of Schur's conjecture in $\mathbb R^d$, Combinatorica (2016)
11. A. B. Kupavskii, M. E. Zhukovskii, Spectra of short monadic sentences about sparse random graphs, Doklady Mathematics  95 (2017),  N1, 60-61.
12. A. Kupavskii, A. Polyanskii, On simplices in diameter graphs in $\mathbb{R}^4$, Mathematical Notes 101 (2017), N2, 232-246.
13. A. Kupavskii, D.A. Shabanov, Colorings of uniform hypergraphs with large girth and applications, to appear in Combinatorics, Probability and Computing.
14. A. Kupavskii, Number of double-normal pairs in space, Discrete and computational Geometry 56 (2016), N3, 711-726.
15. A. Kupavskii, On random subgraphs of Kneser and Schrijver graphs, Journal of Combinatorial Theory, Series A  141 (2016), 8–15.
16. V.V. Bulankina, A.B. Kupavskii, A.A. Polyanskiy, On Schur's conjecture in $\mathbb R^4$, Mathematical Notes 97, N1 (2015), 21–29.
17. A. Kupavskii, D.A. Shabanov, Colorings of Partial Steiner Systems and Their Applications, Journal of Mathematical Sciences 206 (2015), N6, 511–538.
18. A. Kupavskii, Diameter graphs in $\mathbb R^4$, Discrete and Computational Geometry 51, N4 (2014), 842–858.
19. V.V. Bulankina, A.B. Kupavskii, A.A. Polyanskiy, Note on Schur's conjecture in $\mathbb R^4$, Doklady Mathematics 89, N1 (2014), 88–91.
20. N. Alon, A. Kupavskii, Two notions of unit distance graphs, Journal of Combinatorial Theory, Series A 125 (2014), 1–17.
21. A. Kupavskii, Explicit and probabilistic constructions of distance graphs with small clique numbers and large chromatic numbers, Izvestiya: Mathematics 78, N1 (2014), 59–89.
22. A. Kupavskii, M. Titova, Distance Ramsey numbers, Doklady Akademii Nauk 449, N3 (2013), 267–270 (in Russian); Doklady Mathematics 87, N2 (2013), 171–174 (in English).
23. A. Kupavskii, A. Raigorodskii, M. Titova, New bounds for distance Ramsey numbers, Discrete Mathematics 313 (2013), 2566–2574.
24. A.B. Kupavskii, L. Ostroumova, P. Tetali, D. Shabanov, The distribution of second degrees in the Buckley-Osthus random graph model,  Internet Mathematics 9, N4 (2013) 297–335
25. A.B. Kupavskii, A.M.Raigorodskii, Obstructions to the realization of distance graphs with large chromatic numbers on spheres of small radii, Sbornik: Mathematics 204, N10 (2013) 1435–1479.
26. A.B. Kupavskii, D.A. Shabanov, Colorings of partial Steiner systems and their applications, Fundam. Prikl. Mat. 18, N3 (2013),  77–115.
27. D. Il'inskiy, A. Kupavskii, A. Raigorodskii, A. Skopenkov, Discrete analysis for mathematicians and computer scientists, Matematicheskoe Prosveshenie 3, N 17 (2013), 162–181 (In Russian).
28. A.B. Kupavskii, A.M. Raigorodskii, M. Titova, On densest sets without distance one in small-dimensional spaces, Proceedings of Moscow Institute of physics and Technology  4, N1–13 (2012), 111–121 (in Russian).
29. A.B. Kupavskii, E.I. Ponomarenko, A.M. Raigorodskii, On some analogues of Borsuk problem in $\mathbb{Q}^d$, Proceedings of Moscow Institute of physics and Technology 4, N1–13 (2012), 81–90 (in Russian).
30. A.B. Kupavskii, A.M. Raigorodskii, On distance graphs with large chromatic numbers and small clique numbers,  Doklady Mathematics 85, N3 (2012), 394–398.
31. A.B. Kupavskii, D.A. Shabanov, Colorings of uniform hypergraphs with large girth, Doklady Mathematics 85, N2 (2012), 247–250.
32. A.B. Kupavskii, Distance graphs with large chromatic number and arbitrary girth, Moscow Journal of Combinatorics and Number Theory 2, N2 (2012), 52–62.
33. A.B. Kupavskii, A.M. Raigorodskii, Counterexamples to Borsuk's conjecture on spheres of small radii, Moscow Journal of Combinatorics and Number Theory 2, N4 (2012), 27–48.
34. A. Kupavskiy, On the chromatic number of $\mathbb R^n$ with an arbitrary norm, Discrete Mathematics 311 (2011), 437–440.
35. A. Kupavskii, On the coloring of spheres embedded in $\mathbb{R}^n$, Matematicheskiy Sbornik 202, N6 (2011), 83–110 (in Russian); Sbornik: Mathematics 202, N6 (2011), 859–886 (in English).
36. A. Kupavskii, The chromatic number of the space  $\mathbb{R}^n$ with the set of forbidden distances, Doklady Akademii Nauk 435, N6 (2010), 740–743 (in Russian); Doklady Mathematics 82, N3 (2010), 963–966 (in English).
37. A. Kupavskii, A.M. Raigorodskii, Partition of  three-dimensional sets into five parts of smaller diameter, Matematicheskie Zametki 87, N2 (2010), 233–245 (in Russian); Mathematical Notes 87, N2 (2010), 218–229 (in English).
38. A. Kupavskii, Lifting lower bounds of the chromatic number of $\mathbb{R}^n$ in higher dimension, Doklady Akademii Nauk 429, N3 (2009), 305–308 (in Russian); Doklady Mathematics 80, N3 (2009), 833–836 (in English).
39. A. Kupavskiy, A.M. Raigorodskii, About chromatic number of $\mathbb{R}^9$, Fundamentalnaya i Prikladnaya Matematika 14, N5 (2008), 139–154 (in Russian); Journal of mathematical sciences 163, N6 (2008), 720–731 (in English).

## Refereed Conferences Publications

1. N. Frankl, A. Kupavskii, K. Swanepoel, Embedding graphs in Euclidean space, Proceedings of EuroComb'17
2. A. Kupavskii, P. Frankl, Families with no matchings of size $s$, Proceedings of EuroComb'17
3. A. Kupavskii, N. Mustafa, J. Pach, Near-Optimal Lower Bounds for $\epsilon$-nets for Halfspaces and Low Complexity Set Systems, to appear in the Proceedings of The Mathematics of Jiří Matoušek Conference
4. P. Frankl, A. B. Kupavskii, A short proof for an extension of the Erdős-Ko-Rado Theorem, in Proceedings of Connections in Discrete Mathematics conference.
5. A. Kupavskii, N. Mustafa, J. Pach, Lower bounds for the size of $\epsilon$-nets, SoCG'2016.
6. A. Kupavskii, J. Pach, Simultaneous approximation of polynomials, Proceedings of JCDCG^2 (2015).
7. N. Alon, A. Kupavskii, Two notions of unit distance graphs, Proceedings of EuroComb'13.
8. A. Kupavskii, L. Ostroumova, A. Umnov, S. Usachev, P. Serdyukov, G. Gusev, A. Kustarev, Prediction of retweet cascade size over time, Proceedings of the 21st ACM international conference on Information and knowledge management (2012), ACM.
9. A. Kupavskii, A. Umnov, G. Gusev, P. Serdyukov, Predicting the Audience Size of a Tweet, ICWSM'13.
10. A.B. Kupavskii, A.M. Raigorodskii, On the chromatic number of small-dimensional Euclidean spaces, Electronic Notes in Discrete Mathematics, EuroComb'09.

## Books

1. A.A. Glibichuk, A.A. Dainyak, D.G. Il'insliy, A.B. Kupavskii, A.M. Raigorodskii, A.B. Skopenkov, A.A. Chernov, Elements of discrete mathematics in problems, MCCME, 2016 (in Russian).

## Ph.D. thesis

1. A. Kupavskii, Packing and coloring spheres in high-dimensional spaces, Moscow State University, 26.04.2013.
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