Abstract:
Several important aspects of the Nelson-Erdős-Hadwiger classical
problem of combinatorial geometry are considered.
In particular, new lower bounds are obtained for the chromatic numbers
of the spaces Rn and Qn with two, three or four
forbidden distances.
Bibliography: 28 titles.
Citation:
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
\Bibitem{RaiShi08}
\by A.~M.~Raigorodskii, I.~M.~Shitova
\paper Chromatic numbers of real and rational spaces with real or rational forbidden distances
\jour Sb. Math.
\yr 2008
\vol 199
\issue 4
\pages 579--612
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Linking options:
https://www.mathnet.ru/eng/sm3834
https://doi.org/10.1070/SM2008v199n04ABEH003934
https://www.mathnet.ru/eng/sm/v199/i4/p107
This publication is cited in the following 24 articles:
Bau Sh., Johnson P., Noble M., “On Single-Distance Graphs on the Rational Points in Euclidean Spaces”, Can. Math. Bul.-Bul. Can. Math., 64:1 (2021), 13–24
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
E. S. Gorskaya, I. M. Mitricheva, “The chromatic number of the space $(\mathbb R^n, l_1)$”, Sb. Math., 209:10 (2018), 1445–1462
A. A. Sokolov, A. M. Raigorodskii, “O ratsionalnykh analogakh problem Nelsona–Khadvigera i Borsuka”, Chebyshevskii sb., 19:3 (2018), 270–281
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
A. V. Berdnikov, “Estimate for the Chromatic Number of Euclidean Space with Several Forbidden Distances”, Math. Notes, 99:5 (2016), 774–778
S. N. Popova, “Zero-one laws for random graphs with vertices in a Boolean cube”, Siberian Adv. Math., 27:1 (2017), 26–75
A. V. Berdnikov, “Chromatic number with several forbidden distances in the space with the $\ell_q$-metric”, Journal of Mathematical Sciences, 227:4 (2017), 395–401
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
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
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
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
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
A. V. Berdnikov, A. M. Raigorodskii, “On the Chromatic Number of Euclidean Space with Two Forbidden Distances”, Math. Notes, 96:5 (2014), 827–830
A. M. Raigorodskii, D. V. Samirov, “Chromatic Numbers of Spaces with Forbidden Monochromatic Triangles”, Math. Notes, 93:1 (2013), 163–171
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
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
D. V. Samirov, A. M. Raigorodskii, “New lower bounds for the chromatic number of a space with forbidden isosceles triangles”, J. Math. Sci. (N. Y.), 204:4 (2015), 531–541
Andrei M. Raigorodskii, Thirty Essays on Geometric Graph Theory, 2013, 429
I. M. Mitricheva (Shitova), “On the Chromatic Number for a Set of Metric Spaces”, Math. Notes, 91:3 (2012), 399–408
Citation in format AMSBIB
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