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Uspekhi Mat. Nauk, 2000, Volume 55, Issue 2(332), Pages 147–148 (Mi umn281)  

This article is cited in 86 scientific papers (total in 86 papers)

In the Moscow Mathematical Society
Communications of the Moscow Mathematical Society

On the chromatic number of a space

A. M. Raigorodskii

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics


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English version:
Russian Mathematical Surveys, 2000, 55:2, 351–352

Bibliographic databases:

MSC: Primary 52C10; Secondary 05A16, 11B75
Accepted: 26.01.2000

Citation: A. M. Raigorodskii, “On the chromatic number of a space”, Uspekhi Mat. Nauk, 55:2(332) (2000), 147–148; Russian Math. Surveys, 55:2 (2000), 351–352

Citation in format AMSBIB
\by A.~M.~Raigorodskii
\paper On the chromatic number of a~space
\jour Uspekhi Mat. Nauk
\yr 2000
\vol 55
\issue 2(332)
\pages 147--148
\jour Russian Math. Surveys
\yr 2000
\vol 55
\issue 2
\pages 351--352

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    This publication is cited in the following articles:
    1. A. M. Raigorodskii, “Borsuk's problem and the chromatic numbers of some metric spaces”, Russian Math. Surveys, 56:1 (2001), 103–139  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    2. S. A. Bogatyi, “Realization of Configurations and the Loewner Ellipsoid”, Math. Notes, 69:2 (2001), 149–157  mathnet  crossref  crossref  mathscinet  zmath  isi
    3. A. M. Raigorodskii, “The Borsuk and Hadwiger problems and systems of vectors with restrictions on scalar products”, Russian Math. Surveys, 57:3 (2002), 606–607  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    4. Raigorodskii A.M., “The Erdős-Hadwiger problem and the chromatic numbers of finite geometric graphs”, Dokl. Math., 68:2 (2003), 216–220  mathnet  mathscinet  zmath  isi
    5. Raigorodskii A.M., “The problems of Borsuk, Hadwiger, and Grunbaum for some classes of polytopes and graphs”, Dokl. Math., 67:1 (2003), 85–89  mathnet  zmath  isi
    6. Frankl P., Rödl V., “Strong Ramsey properties of simplices”, Israel J. Math., 139 (2004), 215–236  crossref  mathscinet  zmath  isi  scopus  scopus
    7. A. M. Raigorodskii, “On lower bounds for Borsuk and Hadwiger numbers”, Russian Math. Surveys, 59:3 (2004), 585–586  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    8. A. M. Raigorodskii, “The chromatic number of a space with the metric $l_q$”, Russian Math. Surveys, 59:5 (2004), 973–975  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    9. A. M. Raigorodskii, “Colorings of spaces, and random graphs”, J. Math. Sci., 146:2 (2007), 5723–5730  mathnet  crossref  mathscinet  zmath  elib
    10. A. M. Raigorodskii, “The connection between the Borsuk and Erdös–Hadwiger problems”, Russian Math. Surveys, 60:4 (2005), 796–798  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    11. A. M. Raigorodskii, “The Erdős–Hadwiger problem and the chromatic numbers of finite geometric graphs”, Sb. Math., 196:1 (2005), 115–146  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    12. Raigorodskii A.M., “The Nelson-Erdős-Hadwiger problem and embeddings of random graphs into geometric ones”, Dokl. Math., 72:1 (2005), 516–518  mathnet  mathscinet  zmath  isi  elib  elib
    13. A. M. Raigorodskii, “On the Borsuk and Erdös–Hadwiger numbers”, Math. Notes, 79:6 (2006), 854–863  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    14. A. M. Raigorodskii, “On the structure of distance graphs with large chromatic numbers”, Math. Notes, 80:3 (2006), 451–453  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    15. A. M. Raigorodskii, “The Nelson–Erdős–Hadwiger problem and a space realization of a random graph”, Russian Math. Surveys, 61:4 (2006), 783–785  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    16. L. L. Ivanov, “An estimate for the chromatic number of the space $\mathbb R^4$”, Russian Math. Surveys, 61:5 (2006), 984–986  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    17. A. M. Raigorodskii, “On a series of Ramsey-type problems in combinatorial geometry”, Dokl Math, 75:2 (2007), 221  mathnet  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    18. A. M. Raigorodskii, “On distance graphs with large chromatic number but without large simplices”, Russian Math. Surveys, 62:6 (2007), 1224–1225  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    19. A. M. Raigorodskii, “Around Borsuk's Hypothesis”, Journal of Mathematical Sciences, 154:4 (2008), 604–623  mathnet  crossref  mathscinet  zmath  elib
    20. A. M. Raigorodskii, “Chromatic Numbers of Metric Spaces”, Journal of Mathematical Sciences, 154:4 (2008), 624–627  mathnet  crossref  mathscinet  zmath  elib
    21. N. G. Moshchevitin, A. M. Raigorodskii, “Colorings of the Space $\mathbb R^n$ with Several Forbidden Distances”, Math. Notes, 81:5 (2007), 656–664  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    22. O. I. Rubanov, “Chromatic Numbers of 3-Dimensional Distance Graphs Containing No Tetrahedra”, Math. Notes, 82:5 (2007), 718–721  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    23. Shitova I.M., “On the chromatic number of a space with several forbidden distances”, Dokl. Math., 75:2 (2007), 228–230  mathnet  crossref  mathscinet  zmath  isi  elib  elib  scopus
    24. A. M. Raigorodskii, I. M. Shitova, “On the Chromatic Number of Euclidean Space and the Borsuk Problem”, Math. Notes, 83:4 (2008), 579–582  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    25. Carmi P., Dujmović V., Morin P., Wood D.R., “Distinct distances in graph drawings”, Electron. J. Combin., 15:1 (2008), R107, 23 pp.  mathscinet  zmath  isi
    26. A. M. Raigorodskii, I. I. Timirova, “O probleme Nelsona–Erdesha–Khadvigera dlya odnoi serii metricheskikh prostranstv”, Chebyshevskii sb., 9:1 (2008), 158–168  mathnet  mathscinet
    27. A. M. Raigorodskii, I. M. Shitova, “Chromatic numbers of real and rational spaces with real or rational forbidden distances”, Sb. Math., 199:4 (2008), 579–612  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    28. Bachoc Ch., Nebe G., de Oliveira Filho F.M., Vallentin F., “Lower Bounds for Measurable Chromatic Numbers”, Geom. Funct. Anal., 19:3 (2009), 645–661  crossref  mathscinet  zmath  isi  scopus  scopus
    29. E. S. Gorskaya, I. M. Mitricheva (Shitova), V. Yu. Protasov, A. M. Raigorodskii, “Estimating the chromatic numbers of Euclidean space by convex minimization methods”, Sb. Math., 200:6 (2009), 783–801  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    30. A.M. Raigorodskii, O.I. Rubanov, “Small clique and large chromatic number”, Electronic Notes in Discrete Mathematics, 34 (2009), 441  crossref  mathscinet  zmath  scopus  scopus
    31. A. M. Raigorodskii, O. I. Rubanov, “Distance Graphs with Large Chromatic Number and without Large Cliques”, Math. Notes, 87:3 (2010), 392–402  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    32. Jeong-Hyun Kang, Hiren Maharaj, “Distance Graphs fromp-adic Norms”, Integers, 10:4 (2010), 379  crossref  mathscinet  zmath
    33. I. M. Mitricheva (Shitova), “On the Chromatic Number for a Set of Metric Spaces”, Math. Notes, 91:3 (2012), 399–408  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    34. A. B. Kupavskii, A. M. Raigorodskii, “Distance graphs with large chromatic numbers and small clique numbers”, Dokl. Math, 85:3 (2012), 394  crossref  mathscinet  zmath  isi  elib  elib  scopus
    35. Raigorodskii A.M., “On the Chromatic Numbers of Spheres in R-N”, Combinatorica, 32:1 (2012), 111–123  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    36. Zvonarev A.E., Raigorodskii A.M., “O distantsionnykh grafakh s bolshim khromaticheskim i malym klikovym chislami”, Trudy Moskovskogo fiziko-tekhnicheskogo instituta, 4:1-13 (2012), 122–126  elib
    37. Ponomarenko E.I., Raigorodskii A.M., “O khromaticheskom chisle prostranstva q^{n}”, Trudy moskovskogo fiziko-tekhnicheskogo instituta, 4 (2012), 127–130  elib
    38. Raigorodskii A.M., “Predislovie redaktora nomera”, Trudy Moskovskogo fiziko-tekhnicheskogo instituta, 4:1-13 (2012), 4–11  elib
    39. A. M. Raigorodskii, D. V. Samirov, “Chromatic Numbers of Spaces with Forbidden Monochromatic Triangles”, Math. Notes, 93:1 (2013), 163–171  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    40. E. E. Demekhin, A. M. Raigorodskii, O. I. Rubanov, “Distance graphs having large chromatic numbers and containing no cliques or cycles of a given size”, Sb. Math., 204:4 (2013), 508–538  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    41. A. B. Kupavskii, A. M. Raigorodskii, “Obstructions to the realization of distance graphs with large chromatic numbers on spheres of small radii”, Sb. Math., 204:10 (2013), 1435–1479  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    42. E. I. Ponomarenko, A. M. Raigorodskii, “A new lower bound for the chromatic number of the rational space”, Russian Math. Surveys, 68:5 (2013), 960–962  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    43. E. I. Ponomarenko, A. M. Raigorodskii, “New estimates in the problem of the number of edges in a hypergraph with forbidden intersections”, Problems Inform. Transmission, 49:4 (2013), 384–390  mathnet  crossref  isi
    44. A. A. Kokotkin, A. M. Raigorodskii, “On large subgraphs with small chromatic numbers contained in distance graphs”, Journal of Mathematical Sciences, 214:5 (2016), 665–674  mathnet  crossref
    45. M. V. Titova, “One problem on geometric Ramsey numbers”, J. Math. Sci., 201:4 (2014), 527–533  mathnet  crossref  mathscinet  elib
    46. E. I. Ponomarenko, A. M. Raigorodskii, “New Upper Bounds for the Independence Numbers of Graphs with Vertices in $\{-1,0,1\}^n$ and Their Applications to Problems of the Chromatic Numbers of Distance Graphs”, Math. Notes, 96:1 (2014), 140–148  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    47. D. V. Samirov, A. M. Raigorodskii, “New bounds for the chromatic number of a space with forbidden isosceles triangles”, Dokl. Math, 89:3 (2014), 313  crossref  mathscinet  zmath  isi  scopus  scopus
    48. A. A. Kokotkin, “On Large Subgraphs of a Distance Graph Which Have Small Chromatic Number”, Math. Notes, 96:2 (2014), 298–300  mathnet  crossref  mathscinet  zmath  isi  elib
    49. A. E. Zvonarev, A. M. Raigorodskii, D. V. Samirov, A. A. Kharlamova, “On the chromatic number of a space with forbidden equilateral triangle”, Sb. Math., 205:9 (2014), 1310–1333  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    50. A. V. Berdnikov, A. M. Raigorodskii, “On the Chromatic Number of Euclidean Space with Two Forbidden Distances”, Math. Notes, 96:5 (2014), 827–830  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    51. Venkataraman Yegnanarayanan, “Chromatic number of graphs with special distance sets, I”, Algebra Discrete Math., 17:1 (2014), 135–160  mathnet  mathscinet
    52. Exoo G., Ismailescu D., Lim M., “On the Chromatic Number of R-4”, Discret. Comput. Geom., 52:2 (2014), 416–423  crossref  mathscinet  zmath  isi  scopus  scopus
    53. Ponomarenko E.I., Raigorodskii A.M., “An Improvement of the Frankl-Wilson Theorem on the Number of Edges in a Hypergraph With Forbidden Intersections of Edges”, Dokl. Math., 89:1 (2014), 59–60  crossref  mathscinet  zmath  isi  scopus  scopus
    54. E. I. Ponomarenko, A. M. Raigorodskii, “New Lower Bound for the Chromatic Number of a Rational Space with One and Two Forbidden Distances”, Math. Notes, 97:2 (2015), 249–254  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
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    56. A. E. Zvonarev, A. M. Raigorodskii, “Improvements of the Frankl–Rödl theorem on the number of edges of a hypergraph with forbidden intersections, and their consequences in the problem of finding the chromatic number of a space with forbidden equilateral triangle”, Proc. Steklov Inst. Math., 288 (2015), 94–104  mathnet  crossref  crossref  isi  elib  elib
    57. A. V. Bobu, O. A. Kostina, A. E. Kupriyanov, “Independence numbers and chromatic numbers of some distance graphs”, Problems Inform. Transmission, 51:2 (2015), 165–176  mathnet  crossref  isi  elib
    58. Bogolubsky L.I. Raigorodskii A.M., “on the Measurable Chromatic Number of a Space of Dimension N a Parts Per Thousand Currency Sign 24”, 92, no. 3, 2015, 761–763  crossref  mathscinet  zmath  isi  scopus  scopus
    59. Kostina O.A. Raigorodskii A.M., “on Lower Bounds For the Chromatic Number of Sphere”, 92, no. 1, 2015, 500–502  crossref  mathscinet  zmath  isi  scopus  scopus
    60. A. V. Bobu, A. E. Kupriyanov, A. M. Raigorodskii, “Asymptotic study of the maximum number of edges in a uniform hypergraph with one forbidden intersection”, Sb. Math., 207:5 (2016), 652–677  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    61. Raigorodskii A.M., “Combinatorial Geometry and Coding Theory*”, Fundam. Inform., 145:3 (2016), 359–369  crossref  mathscinet  zmath  isi  elib  scopus
    62. A. Sagdeev, “Lower Bounds for the Chromatic Numbers of Distance Graphs with Large Girth”, Math. Notes, 101:3 (2017), 515–528  mathnet  crossref  crossref  mathscinet  isi  elib
    63. A. Sagdeev, “The Chromatic Number of Space with Forbidden Regular Simplex”, Math. Notes, 102:4 (2017), 541–546  mathnet  crossref  crossref  mathscinet  isi  elib
    64. Yu. A. Demidovich, “Lower Bound for the Chromatic Number of a Rational Space with Metric $l_u$ and with One Forbidden Distance”, Math. Notes, 102:4 (2017), 492–507  mathnet  crossref  crossref  mathscinet  isi  elib
    65. A. Ya. Kanel-Belov, V. A. Voronov, D. D. Cherkashin, “On the chromatic number of infinitesimal plane layer”, St. Petersburg Math. J., 29:5 (2018), 761–775  mathnet  crossref  mathscinet  isi  elib
    66. Raigorodskii A.M., Sagdeev A.A., “On the Chromatic Number of a Space With a Forbidden Regular Simplex”, Dokl. Math., 95:1 (2017), 15–16  crossref  mathscinet  zmath  isi  scopus  scopus
    67. A. Sokolov, “On the Chromatic Numbers of Rational Spaces”, Math. Notes, 103:1-2 (2018), 111–117  mathnet  crossref  crossref  mathscinet  isi  elib
    68. R. I. Prosanov, “Upper Bounds for the Chromatic Numbers of Euclidean Spaces with Forbidden Ramsey Sets”, Math. Notes, 103:2 (2018), 243–250  mathnet  crossref  crossref  mathscinet  isi  elib
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    72. A. A. Sagdeev, “Improved Frankl–Rödl theorem and some of its geometric consequences”, Problems Inform. Transmission, 54:2 (2018), 139–164  mathnet  crossref  isi  elib
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    75. A. M. Raigorodskii, T. V. Trukhan, “On the chromatic numbers of some distance graphs”, Dokl. Math., 98:2 (2018), 515–517  mathnet  crossref  crossref  zmath  isi  elib  scopus
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    79. A. V. Bobu, A. E. Kupriyanov, “Refinement of Lower Bounds of the Chromatic Number of a Space with Forbidden One-Color Triangles”, Math. Notes, 105:3 (2019), 329–341  mathnet  crossref  crossref  mathscinet  isi  elib
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    81. Conlon D., Fox J., “Lines in Euclidean Ramsey Theory”, Discret. Comput. Geom., 61:1 (2019), 218–225  crossref  mathscinet  zmath  isi  scopus
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    83. DeCorte E., Golubev K., “Lower Bounds For the Measurable Chromatic Number of the Hyperbolic Plane”, Discret. Comput. Geom., 62:2 (2019), 481–496  crossref  isi
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    86. Bardestani M., Mallahi-Karai K., “Polynomial Configurations in Sets of Positive Upper Density Over Local Fields”, J. Anal. Math., 142:1 (2020), 71–103  crossref  mathscinet  isi
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