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@article{FPM_2013_18_1_a9, author = {M. V. Titova}, title = {One problem on geometric {Ramsey} numbers}, journal = {Fundamentalʹna\^a i prikladna\^a matematika}, pages = {171--180}, publisher = {mathdoc}, volume = {18}, number = {1}, year = {2013}, language = {ru}, url = {http://geodesic.mathdoc.fr/item/FPM_2013_18_1_a9/} }
M. V. Titova. One problem on geometric Ramsey numbers. Fundamentalʹnaâ i prikladnaâ matematika, Tome 18 (2013) no. 1, pp. 171-180. http://geodesic.mathdoc.fr/item/FPM_2013_18_1_a9/
[1] Boltyanskii V. G., Gokhberg I. Ts., Teoremy i zadachi kombinatornoi geometrii, Nauka, M., 1965 | MR
[2] Kupavskii A. B., Raigorodskii A. M., Titova M. V., “O plotneishikh mnozhestvakh bez rasstoyaniya edinitsa v prostranstvakh malykh razmernostei”, Tr. MFTI, 4:1 (2012), 111–121
[3] Kupavskii A. B., Titova M. V., “Distantsionnye chisla Ramseya”, Dokl. RAN, 449:3 (2013), 267–270 | DOI | Zbl
[4] Raigorodskii A. M., “O khromaticheskom chisle prostranstva”, Uspekhi mat. nauk, 55:2 (2000), 147–148 | DOI | MR | Zbl
[5] Raigorodskii A. M., “Problema Borsuka i khromaticheskie chisla metricheskikh prostranstv”, Uspekhi mat. nauk, 56:1 (2001), 107–146 | DOI | MR | Zbl
[6] Raigorodskii A. M., Problema Borsuka, MTsNMO, M., 2006
[7] Raigorodskii A. M., “Vokrug gipotezy Borsuka”, SMFN, 23, 2007, 147–164 | MR | Zbl
[8] Raigorodskii A. M., Lineino-algebraicheskii metod v kombinatorike, MTsNMO, M., 2007 | Zbl
[9] Raigorodskii A. M., “Ob odnoi serii zadach ramseevskogo tipa v kombinatornoi geometrii”, Dokl. RAN, 413:2 (2007), 171–173 | MR | Zbl
[10] Raigorodskii A. M., Titova M. V., “O distantsionnykh podgrafakh grafov v prostranstvakh malykh razmernostei”, Itogi nauki i tekhn. Ser. Sovrem. mat. i eë pril., 20, 2011, 75–83
[11] Kharari F., Teoriya grafov, Mir, M., 1973 | MR
[12] Agarwal P. K., Pach J., Combinatorial Geometry, Wiley-Interscience Ser. Discrete Math. Optimization, Wiley-Interscience, 1995 | MR | Zbl
[13] Alon N., Kupavskii A., Two notions of unit distance graphs, To be submitted
[14] Alon N., Spencer J. H., The Probabilistic Method, Wiley, New York, 2000 | MR | Zbl
[15] Boltyanski V. G., Martini H., Soltan P. S., Excursions into Combinatorial Geometry, Springer, Berlin, 1997 | MR | Zbl
[16] Brass P., Moser W., Pach J., Research Problems in Discrete Geometry, Springer, New York, 2005 | MR
[17] De Bruijn N. G., Erdős P., “A colour problem for infinite graphs and a problem in the theory of relations”, Proc. Konink. Nederl. Akad. Wetensch., Ser. A, 54:5 (1951), 371–373 | Zbl
[18] Conlon D., “A new upper bound for diagonal Ramsey numbers”, Ann. Math., 170 (2009), 941–960 | DOI | MR | Zbl
[19] O'Donnell P., “Arbitrary girth, 4-chromatic unit distance graphs in the plane. I. Graph embedding”, Geombinatorics, 9 (2000), 180–193 | MR | Zbl
[20] O'Donnell P., “Arbitrary girth, 4-chromatic unit distance graphs in the plane. II. Graph description”, Geombinatorics, 9 (2000), 145–152 | MR
[21] Erdős P., “On a set of distances of $n$ points”, Am. Math. Mon., 53 (1946), 248–250 | DOI | MR | Zbl
[22] Erdős P., “Graph theory and probability”, Can. J. Math., 11 (1959), 34–38 | DOI | MR | Zbl
[23] Erdős P., “Unsolved problems”, Proc. Fifth Brit. Comb. Conf. (Univ. Aberdeen, Aberdeen, 1975), Util. Math. Publ., Winnipeg, 1976 | MR
[24] Graham R. L., Rothschild B. L., Spencer J. H., Ramsey Theory, Wiley, New York, 1990 | MR | Zbl
[25] Hadwiger H., “Ein Überdeckungssatz für den Euklidischen Raum”, Portugal. Math., 4 (1944), 140–144 | MR | Zbl
[26] Klee V., Wagon S., Old and New Unsolved Problems in Plane Geometry and Number Theory, Math. Ass. America, 1991 | MR | Zbl
[27] Kupavskii A., Raigorodskii A., Titova M., New bounds for distance Ramsey numbers, Submitted
[28] Larman D. G., Rogers C. A., “The realization of distances within sets in Euclidean space”, Mathematika, 19 (1972), 1–24 | DOI | MR | Zbl
[29] Raigorodskii A. M., “Coloring distance graphs and graphs of diameters”, Thirty Essays on Geometric Graph Theory, ed. J. Pach, Springer, Berlin, 2013, 429–460 | DOI | Zbl
[30] Raigorodskii A. M., Kokotkin A. A., “On large subgraphs of distance graphs having small chromatic number”, Abstracts of the Talks at the Int. Conf. “Fete of Combinatorics and Computer Science”, Keszthely, Hungary, August, 2008
[31] Ramsey F. P., “On a problem of formal logic”, Proc. London Math. Soc. Ser. 2, 30 (1930), 264–286 | DOI | MR
[32] Spencer J., Szemerédi E., Trotter W. T., “Unit distances in the Euclidean plane”, Graph Theory and Combinatorics, ed. B. Bollobás, Academic Press, London, 1984, 293–303 | MR
[33] Székely L. A., “Erdős on unit distances and the Szemerédi–Trotter theorems”, Paul Erdős and his Mathematics, Bolyai Ser., 11, J. Bolyai Math. Soc., Budapest, 2002, 649–666 | MR | Zbl
[34] Wormald N., “A 4-chromatic graph with a special plane drawing”, Austral. Math. Soc., Ser. A, 28 (1979), 1–8 | DOI | MR | Zbl