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Uspekhi Mat. Nauk, 2001, Volume 56, Issue 1(337), Pages 107–146 (Mi umn358)  

This article is cited in 164 scientific papers (total in 165 papers)

Borsuk's problem and the chromatic numbers of some metric spaces

A. M. Raigorodskii

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

Abstract: A detailed survey is given of various results pertaining to two well-known problems of combinatorial geometry: Borsuk's problem on partitions of an arbitrary bounded $d$-dimensional set of non-zero diameter into parts of smaller diameter, and the problem of finding chromatic numbers of some metric spaces. Furthermore, a general method is described for obtaining good lower bounds for the minimum number of parts of smaller diameter into which an arbitrary non-singleton set of dimension $d$ can be divided as well as for the chromatic numbers of various metric spaces, in particular, $\mathbb R^d$ and $\mathbb Q^d$. Finally, some new lower bounds are proved for chromatic numbers in low dimensions, and new natural generalizations of the notion of chromatic number are proposed.

DOI: https://doi.org/10.4213/rm358

Full text: PDF file (513 kB)
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English version:
Russian Mathematical Surveys, 2001, 56:1, 103–139

Bibliographic databases:

UDC: 514.17+519.174
MSC: Primary 51M15, 54E35, 51M20, 05C15; Secondary 52A20, 52C10
Received: 07.12.2000

Citation: A. M. Raigorodskii, “Borsuk's problem and the chromatic numbers of some metric spaces”, Uspekhi Mat. Nauk, 56:1(337) (2001), 107–146; Russian Math. Surveys, 56:1 (2001), 103–139

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    This publication is cited in the following articles:
    1. 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
    2. A. M. Raigorodskii, “The Borsuk problem for integral polytopes”, Sb. Math., 193:10 (2002), 1535–1556  mathnet  crossref  crossref  mathscinet  zmath  isi
    3. Raigorodskii A.M., “Borsuk's problem for $(0,1)$-polytopes and cross-polytopes”, Dokl. Math., 65:3 (2002), 413–416  mathnet  mathscinet  zmath  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. Hinrichs A., Richter Ch., “New sets with large Borsuk numbers”, Discrete Math., 270:1-3 (2003), 137–147  crossref  mathscinet  zmath  isi  scopus
    6. Raigorodskii A.M., “The problem of Borsuk, Hadwinger, and Grunbaum for some classes of polytopes and graphs”, Dokl. Math., 67:1 (2003), 85–89  mathnet  mathscinet  zmath  isi
    7. A. M. Raigorodskii, Yu. A. Kalnishkan, “On Borsuk"s Problem in $\mathbb R^3$”, Math. Notes, 74:1 (2003), 144–146  mathnet  crossref  crossref  mathscinet  zmath  isi
    8. 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
    9. 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
    10. Raigorodskii A.M., “The Borsuk partition problem: the seventieth anniversary”, Math. Intelligencer, 26:3 (2004), 4–12  crossref  mathscinet  zmath  isi  elib  scopus
    11. Furedi Z., Kang Jeong-Hyun, “Distance graph on $\mathbb Z^n$ with $l_1$ norm”, Theoret. Comput. Sci., 319:1-3 (2004), 357–366  crossref  mathscinet  zmath  isi  scopus  scopus
    12. Martini H., Swanepoel K.J., “The geometry of Minkowski spaces—a survey. II”, Expo. Math., 22:2 (2004), 93–144  crossref  mathscinet  zmath  isi  scopus  scopus
    13. Frankl P., Rödl V., “Strong Ramsey properties of simplices”, Israel J. Math., 139 (2004), 215–236  crossref  mathscinet  zmath  isi  scopus  scopus
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    18. 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
    19. Elsholtz C., Klotz W., “Maximal dimension of unit simplices”, Discrete Comput. Geom., 34:1 (2005), 167–177  crossref  mathscinet  zmath  isi  scopus
    20. A. M. Raigorodskii, “On the Borsuk and Erdös–Hadwiger numbers”, Math. Notes, 79:6 (2006), 854–863  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    21. 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
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    34. 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
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    70. M. E. Zhukovskii, “A weak zero-one law for sequences of random distance graphs”, Sb. Math., 203:7 (2012), 1012–1044  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
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    88. A. B. Kupavskii, M. V. Titova, “Distance ramsey numbers”, Dokl. Math, 87:2 (2013), 171  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    89. A.B.. Kupavskii, A.M.. Raigorodskii, M.V.. Titova, “New bounds for the distance Ramsey number”, Discrete Mathematics, 313:22 (2013), 2566  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    90. E.I.. Ponomarenko, A.M.. Raigorodskii, “A new intersection theorem and its applications to bounding the chromatic numbers of spaces”, Electronic Notes in Discrete Mathematics, 43 (2013), 241  crossref  scopus  scopus
    91. 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
    92. 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
    93. 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
    94. 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
    95. V. O. Manturov, “On the chromatic numbers of integer and rational lattices”, Journal of Mathematical Sciences, 214:5 (2016), 687–698  mathnet  crossref
    96. M. V. Titova, “One problem on geometric Ramsey numbers”, J. Math. Sci., 201:4 (2014), 527–533  mathnet  crossref  mathscinet  elib
    97. A. B. Kupavskii, “Explicit and probabilistic constructions of distance graphs with small clique numbers and large chromatic numbers”, Izv. Math., 78:1 (2014), 59–89  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    98. V. V. Bulankina, A. B. Kupavskii, A. A. Polyanskii, “On Schur’s conjecture in ℝ4”, Dokl. Math, 89:1 (2014), 88  crossref  mathscinet  zmath  isi
    99. S. N. Popova, “Zero-one law for random distance graphs with vertices in $\{-1,0,1\}^n$”, Problems Inform. Transmission, 50:1 (2014), 57–78  mathnet  crossref  isi
    100. Andrey Kupavskii, “Diameter Graphs in
      $${\mathbb R}^4$$
      R 4”, Discrete Comput Geom, 2014  crossref  mathscinet  isi
    101. 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
    102. 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
    103. 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
    104. V. P. Filimonov, “Covering sets in $\mathbb{R}^m$”, Sb. Math., 205:8 (2014), 1160–1200  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    105. 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
    106. A. E. Zvonarev, A. M. Raigorodskii, D. V. Samirov, A. A. Kharlamova, “Improvement of the Frankl-Rödl theorem on the number of edges in hypergraphs with forbidden cardinalities of edge intersections”, Dokl. Math, 90:1 (2014), 432  crossref  mathscinet  zmath  isi
    107. L. I. Bogolyubskii, A. S. Gusev, M. M. Pyaderkin, A. M. Raigorodskii, “Independence numbers and chromatic numbers of random subgraphs in some sequences of graphs”, Dokl. Math, 90:1 (2014), 462  crossref  mathscinet  zmath  isi  scopus  scopus
    108. 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
    109. Venkataraman Yegnanarayanan, “Chromatic number of graphs with special distance sets, I”, Algebra Discrete Math., 17:1 (2014), 135–160  mathnet  mathscinet
    110. Kokotkin A.A., “Realization of Subgraphs of Random Graphs By Graphs of Diameters in Euclidean Spaces”, Dokl. Math., 89:3 (2014), 362–364  crossref  mathscinet  zmath  isi
    111. 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
    112. V. V. Bulankina, A. B. Kupavskii, A. A. Polyanskii, “On Schur's Conjecture in $\mathbb R^4$”, Math. Notes, 97:1 (2015), 21–29  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    113. 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
    114. M. E. Zhukovskii, A. M. Raigorodskii, “Random graphs: models and asymptotic characteristics”, Russian Math. Surveys, 70:1 (2015), 33–81  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    115. A. S. Gusev, “New Upper Bound for the Chromatic Number\of a Random Subgraph of a Distance Graph”, Math. Notes, 97:3 (2015), 326–332  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    116. 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
    117. A. A. Kokotkin, A. M. Raigorodskii, “On the Realization of Subgraphs of a Random Graph by Diameter Graphs in Euclidean Spaces”, Math. Notes, 97:5 (2015), 709–724  mathnet  crossref  crossref  mathscinet  isi  elib
    118. V. V. Utkin, “Hamiltonian Paths in Distance Graphs”, Math. Notes, 97:6 (2015), 919–929  mathnet  crossref  crossref  mathscinet  isi  elib
    119. A. V. Krot, A. M. Raigorodskii, “O realizatsii sluchainykh grafov grafami rasstoyanii i diametrov v evklidovykh prostranstvakh”, Chebyshevskii sb., 16:2 (2015), 133–143  mathnet  elib
    120. 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
    121. M. M. Pyaderkin, “On the stability of the Erdös-Ko-Rado theorem”, Dokl. Math, 91:3 (2015), 290  crossref  mathscinet  zmath  isi
    122. A. M. Raigorodskii, “Lovász' Theorem on the Chromatic Number of Spheres Revisited”, Math. Notes, 98:3 (2015), 522–524  mathnet  crossref  crossref  mathscinet  isi  elib
    123. L. I. Bogolubsky, A. S. Gusev, M. M. Pyaderkin, A. M. Raigorodskii, “Independence numbers and chromatic numbers of the random subgraphs of some distance graphs”, Sb. Math., 206:10 (2015), 1340–1374  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    124. A. V. Burkin, “Small subgraphs in random distance graphs”, Theory Probab. Appl., 60:3 (2016), 367–382  mathnet  crossref  crossref  mathscinet  isi  elib
    125. A. V. Burkin, “The threshold probability for the property of planarity of a random subgraph of a regular graph”, Russian Math. Surveys, 70:6 (2015), 1170–1172  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    126. 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
    127. Bobu A.V., Kupriyanov A.E., Raigorodskii A.M., “on the Maximal Number of Edges in a Uniform Hypergraph With One Forbidden Intersection”, 92, no. 1, 2015, 401–403  crossref  mathscinet  zmath  isi  scopus  scopus
    128. Krot A.V., “on Threshold Probabilities For the Realization of a Random Graph By a Geometric Graph”, 92, no. 1, 2015, 480–481  crossref  mathscinet  zmath  isi  scopus  scopus
    129. 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
    130. Ph. A. Pushnyakov, “A new estimate for the number of edges in induced subgraphs of a special distance graph”, Problems Inform. Transmission, 51:4 (2015), 371–377  mathnet  crossref  isi  elib
    131. M. M. Pyaderkin, “Independence Numbers of Random Subgraphs of a Distance Graph”, Math. Notes, 99:2 (2016), 312–319  mathnet  crossref  crossref  mathscinet  isi  elib
    132. S. N. Popova, “Zero-one law for random subgraphs of some distance graphs with vertices in $\mathbb Z^n$”, Sb. Math., 207:3 (2016), 458–478  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    133. Ph. Pushnyakov, “On the Number of Edges in Induced Subgraphs of a Special Distance Graph”, Math. Notes, 99:4 (2016), 545–551  mathnet  crossref  crossref  mathscinet  isi  elib
    134. M. M. Pyaderkin, “Independence Numbers of Random Subgraphs of Distance Graphs”, Math. Notes, 99:4 (2016), 556–563  mathnet  crossref  crossref  mathscinet  isi  elib
    135. 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
    136. A. V. Berdnikov, “Estimate for the Chromatic Number of Euclidean Space with Several Forbidden Distances”, Math. Notes, 99:5 (2016), 774–778  mathnet  crossref  crossref  mathscinet  isi  elib
    137. S. N. Popova, “Zero-one laws for random graphs with vertices in a Boolean cube”, Siberian Adv. Math., 27:1 (2017), 26–75  mathnet  crossref  crossref  mathscinet  elib
    138. A. V. Bobu, A. E. Kupriyanov, “On chromatic numbers of close-to-Kneser distance graphs”, Problems Inform. Transmission, 52:4 (2016), 373–390  mathnet  crossref  isi  elib
    139. Tikhomirov M., “On computational complexity of length embeddability of graphs”, Discrete Math., 339:11 (2016), 2605–2612  crossref  mathscinet  zmath  isi  elib  scopus
    140. Tikhomirov M.I., “On the distance and multidistance graph embeddability problem”, Dokl. Math., 93:3 (2016), 280–281  crossref  mathscinet  zmath  isi  elib  scopus
    141. Raigorodskii A.M., “Combinatorial Geometry and Coding Theory*”, Fundam. Inform., 145:3 (2016), 359–369  crossref  mathscinet  zmath  isi  elib  scopus
    142. A. B. Kupavskii, A. A. Poljanskij, “On Simplices in Diameter Graphs in $\mathbb R^4$”, Math. Notes, 101:2 (2017), 265–276  mathnet  crossref  crossref  mathscinet  isi  elib
    143. 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
    144. A. Sagdeev, “The Chromatic Number of Space with Forbidden Regular Simplex”, Math. Notes, 102:4 (2017), 541–546  mathnet  crossref  crossref  mathscinet  isi  elib
    145. 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
    146. 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
    147. Bobu A.V., Kupriyanov A.E., Raigorodskii A.M., “On the Number of Edges in a Uniform Hypergraph With a Range of Permitted Intersections”, Dokl. Math., 96:1 (2017), 354–357  crossref  mathscinet  zmath  isi  scopus  scopus
    148. Cherkashin D.D. Raigorodskii A.M., “On the Chromatic Numbers of Low-Dimensional Spaces”, Dokl. Math., 95:1 (2017), 5–6  crossref  mathscinet  zmath  isi  scopus  scopus
    149. 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
    150. A. V. Bobu, A. E. Kupriyanov, A. M. Raigorodskii, “On the number of edges of a uniform hypergraph with a range of allowed intersections”, Problems Inform. Transmission, 53:4 (2017), 319–342  mathnet  crossref  isi  elib
    151. A. Sokolov, “On the Chromatic Numbers of Rational Spaces”, Math. Notes, 103:1-2 (2018), 111–117  mathnet  crossref  crossref  mathscinet  isi  elib
    152. A. V. Burkin, M. E. Zhukovskii, “Small subgraphs and their extensions in a random distance graph”, Sb. Math., 209:2 (2018), 163–186  mathnet  crossref  crossref  adsnasa  isi  elib
    153. 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  isi  elib
    154. Frankl P., Kupayskii A., “Erdos-Ko-Rado Theorem For (0, +/- 1)-Vectors”, J. Comb. Theory Ser. A, 155 (2018), 157–179  crossref  mathscinet  zmath  isi
    155. Cherkashin D. Kulikov A. Raigorodskii A., “On the Chromatic Numbers of Small-Dimensional Euclidean Spaces”, Discrete Appl. Math., 243 (2018), 125–131  crossref  mathscinet  zmath  isi  scopus  scopus
    156. Frankl P., “An Exact Result For (0, +/- 1)-Vectors”, Optim. Lett., 12:5 (2018), 1011–1017  crossref  mathscinet  zmath  isi  scopus  scopus
    157. Frankl P., Kupavskii A., “Families of Vectors Without Antipodal Pairs”, Stud. Sci. Math. Hung., 55:2 (2018), 231–237  crossref  mathscinet  zmath  isi  scopus  scopus
    158. E. S. Gorskaya, I. M. Mitricheva, “The chromatic number of the space $(\mathbb R^n, l_1)$”, Sb. Math., 209:10 (2018), 1445–1462  mathnet  crossref  crossref  isi  elib
    159. A. Sagdeev, “On the Frankl–Rödl theorem”, Izv. Math., 82:6 (2018), 1196–1224  mathnet  crossref  crossref  adsnasa  isi  elib
    160. A. A. Sagdeev, “Exponentially Ramsey sets”, Problems Inform. Transmission, 54:4 (2018), 372–396  mathnet  crossref  isi
    161. O. A. Kostina, “On Lower Bounds for the Chromatic Number of Spheres”, Math. Notes, 105:1 (2019), 16–27  mathnet  crossref  crossref  isi  elib
    162. L. I. Bogolubsky, A. M. Raigorodskii, “A Remark on Lower Bounds for the Chromatic Numbers of Spaces of Small Dimension with Metrics $\ell_1$ and $\ell_2$”, Math. Notes, 105:2 (2019), 180–203  mathnet  crossref  crossref  isi  elib
    163. A. V. Bobu, A. E. Kupriyanov, “Uluchshenie nizhnikh otsenok khromaticheskogo chisla prostranstva s zapreschennymi odnotsvetnymi treugolnikami”, Matem. zametki, 105:3 (2019), 349–363  mathnet  crossref  elib
    164. F. A. Pushnyakov, “O kolichestvakh reber v porozhdennykh podgrafakh nekotorykh distantsionnykh grafov”, Matem. zametki, 105:4 (2019), 592–602  mathnet  crossref  elib
    165. R. I. Prosanov, “Kontrprimery k gipoteze Borsuka, imeyuschie bolshoi obkhvat”, Matem. zametki, 105:6 (2019), 890–898  mathnet  crossref
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