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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

DOI: https://doi.org/10.4213/rm281

Full text: PDF file (226 kB)
References: PDF file   HTML file

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
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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
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    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
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    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
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    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
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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
    80. R. I. Prosanov, “Counterexamples to Borsuk's Conjecture with Large Girth”, Math. Notes, 105:6 (2019), 874–880  mathnet  crossref  crossref  mathscinet  isi  elib
    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
    84. Sagdeev A.A., Raigorodskii A.M., “on a Frankl-Wilson Theorem and Its Geometric Corollaries”, Acta Math. Univ. Comen., 88:3 (2019), 1029–1033  isi
    85. Naslund E., “Monochromatic Equilateral Triangles in the Unit Distance Graph”, Bull. London Math. Soc., 52:4 (2020), 687–692  crossref  mathscinet  isi
    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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