Voir la notice de l'article provenant de la source Math-Net.Ru
@article{MZM_2017_102_4_a9, author = {A. Sagdeev}, title = {The {Chromatic} {Number} of {Space} with {Forbidden} {Regular} {Simplex}}, journal = {Matemati\v{c}eskie zametki}, pages = {579--585}, publisher = {mathdoc}, volume = {102}, number = {4}, year = {2017}, language = {ru}, url = {http://geodesic.mathdoc.fr/item/MZM_2017_102_4_a9/} }
A. Sagdeev. The Chromatic Number of Space with Forbidden Regular Simplex. Matematičeskie zametki, Tome 102 (2017) no. 4, pp. 579-585. http://geodesic.mathdoc.fr/item/MZM_2017_102_4_a9/
[1] A. Soifer, “Khromaticheskoe chislo ploskosti: ego proshloe, nastoyaschee i buduschee”, Matem. prosv., ser. 3, 8, Izd-vo MTsNMO, M., 2004, 186–221
[2] A. M. Raigorodskii, “O khromaticheskom chisle prostranstva”, UMN, 55:2 (332) (2000), 147–148 | DOI | MR | Zbl
[3] D. G. Larman, C. A. Rogers, “The realization of distances within sets in Euclidean space”, Mathematika, 19 (1972), 1–24 | DOI | MR | Zbl
[4] R. L. Graham, B. L. Rothschild, J. H. Spencer, Ramsey Theory, John Wiley and Sons, New York, 1990 | MR | Zbl
[5] P. Frankl, V. Rödl, “All triangles are Ramsey”, Trans. Amer. Math. Soc., 297:2 (1986), 777–779 | DOI | MR | Zbl
[6] P. Frankl, V. Rödl, “Forbidden intersections”, Trans. of Amer. Math. Soc., 300:1 (1987), 259–286 | DOI | MR | Zbl
[7] P. Frankl, V. Rödl, “A partition property of simplices in Euclidean space”, J. Amer. Math. Soc., 3:1 (1990), 1–7 | DOI | MR | Zbl
[8] A. E. Zvonarëv, A. M. Raigorodskii, D. V. Samirov, A. A. Kharlamova, “O khromaticheskom chisle prostranstva s zapreschennym ravnostoronnim treugolnikom”, Matem. sb., 205:9 (2014), 97–120 | DOI | MR | Zbl
[9] A. E. Zvonarev, A. M. Raigorodskii, D. V. Samirov, A. A. Kharlamova, “Uluchshenie teoremy Frankla–Redlya o chisle reber gipergrafa s zapretami na peresecheniya”, Dokl. AN, 457:2 (2014), 144–146 | DOI | MR | Zbl
[10] A. A. Sagdeev, “O nizhnikh otsenkakh khromaticheskikh chisel distantsionnykh grafov s bolshim obkhvatom”, Matem. zametki, 101:3 (2017), 430–445 | DOI | MR
[11] A. E. Zvonarev, A. M. Raigorodskii, “Uluchsheniya teoremy Frankla–Redlya o chisle reber gipergrafa s zapreschennym peresecheniem i ikh sledstviya v zadache o khromaticheskom chisle prostranstva s zapreschennym ravnostoronnim treugolnikom”, Geometriya, topologiya i prilozheniya, Tr. MIAN, 288, MAIK, M., 2015, 109–119 | DOI | MR | Zbl
[12] A. B. Kupavskii, “Distance graphs with large chromatic number and arbitrary girth”, Mosc. J. Comb. Number Theory, 2:2 (2012), 52–62 | MR | Zbl
[13] A. M. Raigorodskii, “O distantsionnykh grafakh, imeyuschikh bolshoe khromaticheskoe chislo, no ne soderzhaschikh bolshikh simpleksov”, UMN, 62:6 (378) (2007), 187–188 | DOI | MR | Zbl
[14] A. M. Raigorodskii, O. I. Rubanov, “Small clique and large chromatic number”, European Conference on Combinatorics, Graph Theory and Applications, Electron. Notes Discrete Math., 34, Elsevier Sci. B. V., Amsterdam, 2009, 441–445 | DOI | MR | Zbl
[15] A. M. Raigorodskii, O. I. Rubanov, “On the clique and the chromatic numbers of high-dimensional distance graphs”, Number Theory and Applications, Hindustan Book Agency, New Delhi, 2009, 149–157 | MR | Zbl
[16] A. M. Raigorodskii, O. I. Rubanov, “O grafakh rasstoyanii s bolshim khromaticheskim chislom i bez bolshikh klik”, Matem. zametki, 87:3 (2010), 417–428 | DOI | MR | Zbl
[17] A. B. Kupavskii, A. M. Raigorodskii, “O distantsionnykh grafakh s bolshim khromaticheskim i malym klikovym chislami”, Dokl. AN, 444:5 (2012), 483–487 | MR | Zbl
[18] A. E. Zvonarev, A. M. Raigorodskii, “O distantsionnykh grafakh s bolshim khromaticheskim i malym klikovym chislami”, Tr. MFTI, 4:1 (2012), 122–126
[19] A. B. Kupavskii, A. M. Raigorodskii, “O prepyatstviyakh k realizatsii distantsionnykh grafov s bolshim khromaticheskim chislom na sferakh malogo radiusa”, Matem. sb., 204:10 (2013), 47–90 | DOI | MR | Zbl
[20] E. E. Demekhin, A. M. Raigorodskii, O. I. Rubanov, “Distantsionnye grafy, imeyuschie bolshoe khromaticheskoe chislo i ne soderzhaschie klik ili tsiklov zadannogo razmera”, Matem. sb., 204:4 (2013), 49–78 | DOI | MR | Zbl
[21] A. B. Kupavskii, “Yavnye i veroyatnostnye konstruktsii distantsionnykh grafov s malenkim klikovym i bolshim khromaticheskim chislami”, Izv. RAN. Ser. matem., 78:1 (2014), 65–98 | DOI | MR | Zbl
[22] N. Alon, A. Kupavskii, “Two notions of unit distance graphs”, J. Combin. Theory Ser. A, 125 (2014), 1–17 | DOI | MR | Zbl
[23] D. D. Cherkashin, A. M. Raigorodskii, “O khromaticheskikh chislakh prostranstv maloi razmernosti”, Dokl. AN, 472:1 (2017), 11–12 | Zbl
[24] A. M. Raigorodskii, D. V. Samirov, “Novye otsenki v zadache o khromaticheskom chisle prostranstva s zapreschennymi ravnobedrennymi treugolnikami”, Dokl. AN, 456:3 (2014), 280–283 | MR | Zbl
[25] P. K. Agarwal, J. Pach, Combinatorial Geometry, John Wiley and Sons, New York, 1995 | MR | Zbl
[26] P. Brass, W. Moser, J. Pach, Research Problems in Discrete Geometry, Springer, New York, 2005 | MR | Zbl
[27] A. Soifer, “The Mathematical Coloring Book”, Springer, 2009, New York | MR | Zbl
[28] A. M. Raigorodskii, “Problema Borsuka i khromaticheskie chisla nekotorykh metricheskikh prostranstv”, UMN, 56:1 (337) (2001), 107–146 | DOI | MR | Zbl
[29] A. M. Raigorodskii, “Vokrug gipotezy Borsuka”, Geometriya i mekhanika, SMFN, 23, RUDN, M., 2007, 147–164 | MR | Zbl
[30] A. M. Raigorodskii, “Coloring distance graphs and graphs of diameters”, Thirty Essays on Geometric Graph Theory, Springer, New York, 2013, 429–460 | DOI | MR | Zbl
[31] A. M. Raigorodskii, “Cliques and cycles in distance graphs and graphs of diameters”, Discrete Geometry and Algebraic Combinatorics, Contemp. Math., 625, Amer. Math. Soc., Providence, RI, 2014, 93–109 | MR | Zbl
[32] K. Prakhar, Raspredelenie prostykh chisel, Mir, M., 1967 | MR | Zbl
[33] R. C. Baker, G. Harman, J. Pintz, “The difference between consecutive primes. II”, Proc. London Math. Soc. (3), 83:3 (2001), 532–562 | DOI | MR | Zbl
[34] P. Frankl, R. M. Wilson, “Intersection theorems with geometric consequences”, Combinatorica, 1:4 (1981), 357–368 | DOI | MR | Zbl