Geodesic
On dividing sets into parts of smaller diameter
Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ, Tome 495 (2020), pp. 74-77 Cet article a éte moissonné depuis la source Math-Net.Ru

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An important generalization of Borsuk's classical problem of partitioning sets into parts of smaller diameter is studied. New upper and lower bounds for the Borsuk numbers are found.
Mots-clés : partition
Keywords: coloring, point sets in spaces, diameter graph. 
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     author = {A. M. Raigorodskii},
     title = {On dividing sets into parts of smaller diameter},
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A. M. Raigorodskii. On dividing sets into parts of smaller diameter. Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ, Tome 495 (2020), pp. 74-77. http://geodesic.mathdoc.fr/item/DANMA_2020_495_a15/

[1] Raigorodskii A.M., “Cliques and cycles in distance graphs and graphs of diameters”, Discrete Geometry and Algebraic Combinatorics, Contemporary Mathematics, 625, AMS, 2014, 93–109 | DOI | MR | Zbl

[2] Bogolyubskii L.I., Raigorodskii A.M., “Zamechanie o nizhnikh otsenkakh khromaticheskikh chisel prostranstv maloi razmernosti s metrikami $l_1$ i $l_2$”, Matem. Zametki, 105:2 (2019), 187–213 | DOI | MR | Zbl

[3] Filimonov V.P., “O pokrytii mnozhestv v ${{\mathbb{R}}^{m}}$”, Matem. sb., 205:8 (2014), 95–138 | DOI | Zbl

[4] Rogers C.A., “Covering a sphere with spheres”, Mathematika, 10 (1963), 157–164 | DOI | MR | Zbl

[5] Bourgain J., Lindenstrauss J., “On covering a set in ${{\mathbb{R}}^{d}}$ by balls of the same diameter”, Geometric Aspects of Functional Analysis, Lecture Notes in Math., 1469, eds. J. Lindenstrauss, V. Milman, Springer-Verlag, Berlin, 1991, 138–144 | DOI | MR

[6] Ahlswede R., Khachatrian L.H., “The complete intersection theorem for systems of finite sets”, Europ. J. Combin., 18 (1997), 125–136 | DOI | MR | Zbl

[7] Raigorodskii A.M., Kharlamova A.A., “O sovokupnostyakh (-1, 0, 1)-vektorov s zapretami na velichiny poparnykh skalyarnykh proizvedenii”, Trudy po vektornomu i tenzornomu analizu, 29, Izd-vo MGU, M., 2013, 130–146

[8] Frankl P., Kupavskii A., “Erdős-Ko-Rado theorem for ${\text{\{ }}0, \pm 1{\text{\} }}$-vectors”, J. Comb. Theory Ser. A, 155 (2018), 157–179 | DOI | MR | Zbl

[9] Frankl P., Kupavskii A., “Incompatible intersection properties”, Combinatorica, 39:6 (2019), 1255–1266 | DOI | MR | Zbl

[10] Kupavskii A., “Degree versions of theorems on intersecting families via stability”, J. Comb. Theory Ser. A, 168 (2019), 272–287 | DOI | MR | Zbl

[11] Kupavskii A.B., Sagdeev A.A., “Teoriya Ramseya v prostranstve s chebyshevskoi metrikoi”, UMN, 75:5 (455) (2020), 191–192 | DOI | MR | Zbl

[12] Bobu A.V., Kupriyanov A.E., Raigorodskii A.M., “Ob odnom obobschenii knezerovskikh grafov”, Matem. zametki, 107:3 (2020), 351–365 | DOI | MR | Zbl

[13] Raigorodskii A.M., Sagdeev A.A., “On a Frankl-Wilson theorem and its geometric corollaries”, Acta Math. Univ. Comenianae, 88:3 (2019), 1029–1033 | MR

[14] Raigorodskii A.M., Shishunov E.D., “O chislakh nezavisimosti nekotorykh distantsionnykh grafov s vershinami v $\{-1, 0, 1\}^n$”, DAN, 485:3 (2019), 269–271 | Zbl

[15] Pushnyakov F.A., Raigorodskii A.M., “Otsenka chisla reber v osobykh podgrafakh nekotorogo distantsionnogo grafa”, Matem. zametki, 107:2 (2020), 286–298 | DOI | MR | Zbl