Geodesic
Zero-one law for random subgraphs of some distance graphs with vertices in $\mathbb Z^n$
Sbornik. Mathematics, Tome 207 (2016) no. 3, pp. 458-478 Cet article a éte moissonné depuis la source Math-Net.Ru

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The zero-one law for the model of random distance graphs with vertices in $\mathbb Z^n$ is studied. Sufficient conditions for a sequence of random distance graphs to obey the zero-one law are derived, as well as conditions under which it contains a subsequence obeying the zero-one law. Bibliography: 20 titles.
Keywords: random graphs, zero-one law, distance graphs. 
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S. N. Popova. Zero-one law for random subgraphs of some distance graphs with vertices in $\mathbb Z^n$. Sbornik. Mathematics, Tome 207 (2016) no. 3, pp. 458-478. http://geodesic.mathdoc.fr/item/SM_2016_207_3_a7/

[1] Yu. V. Glebskii, D. I. Kogan, M. I. Liogonkii, V. A. Talanov, “Ob'em i dolya vypolnimosti formul uzkogo ischisleniya predikatov”, Kibernetika, 1969, no. 2, 17–27 | MR | Zbl

[2] M. E. Zhukovskii, “Oslablennyi zakon “nulya ili edinitsy” dlya sluchainykh distantsionnykh grafov”, Vestnik RUDN. Seriya Matematika. Informatika. Fizika, 2010, no. 2 (1), 11–25

[3] M. E. Zhukovskii, “The weak zero-one laws for the random distance graphs”, Dokl. Math., 81:1 (2010), 51–54 | DOI | MR | Zbl

[4] M. E. Zhukovskii, “The weak zero-one law for the random distance graphs”, Theory Probab. Appl., 55:2 (2011), 356–360 | DOI | DOI | MR | Zbl

[5] M. E. Zhukovskii, “On a sequence of random distance graphs subject to the zero-one law”, Probl. Inf. Transm., 47:3 (2011), 251–268 | DOI | MR | Zbl

[6] M. E. Zhukovskii, “A weak zero-one law for sequences of random distance graphs”, Sb. Math., 203:7 (2012), 1012–1044 | DOI | DOI | MR | Zbl

[7] S. N. Popova, “Zero-one law for random distance graphs with vertices in $\{-1,0,1\}^n$”, Probl. Inf. Transm., 50:1 (2014), 57–78 | DOI | MR | Zbl

[8] A. M. Raigorodskii, “Borsuk's problem and the chromatic numbers of some metric spaces”, Russian Math. Surveys, 56:1 (2001), 103–139 | DOI | DOI | MR | Zbl

[9] A. M. Raigorodskii, “The Borsuk problem for integral polytopes”, Sb. Math., 193:10 (2002), 1535–1556 | DOI | DOI | MR | Zbl

[10] 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 | DOI | DOI | MR | Zbl

[11] A. M. Raigorodskii, “The Erdős–Hadwiger problem and the chromatic numbers of finite geometric graphs”, Sb. Math., 196:1 (2005), 115–146 | DOI | DOI | MR | Zbl

[12] A. M. Raigorodskii, “The problems of Borsuk and Grünbaum on lattice polytopes”, Izv. Math., 69:3 (2005), 513–537 | DOI | DOI | MR | Zbl

[13] 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 | DOI | DOI | MR | Zbl

[14] E. S. Gorskaya, I. M. Mitricheva (Shitova), V. Yu. Protasov, A. M. Raigorodskii, “Estimating the chromatic numbers of Euclidean space by convex minimization methods”, Sb. Math., 200:6 (2009), 783–801 | DOI | DOI | MR | Zbl

[15] 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 | DOI | DOI | MR | Zbl

[16] F. J. MacWilliams, N. J. A. Sloane, The theory of error-correcting codes, Parts I, II, North-Holland Math. Library, 16, North-Holland Publishing Co., Amsterdam–New York–Oxford, 1977 | MR | MR | Zbl | Zbl

[17] N. K. Vereschagin, A. Shen, Yazyki i ischisleniya, MTsNMO, M., 2000, 286 pp.

[18] N. Alon, J. H. Spencer, The probabilistic method, Wiley-Intersci. Ser. Discrete Math. Optim., 2nd ed., Wiley-Interscience [John Wiley Sons], New York, 2000, xviii+301 pp. | DOI | MR | Zbl

[19] A. M. Raigorodskii, Modeli sluchainykh grafov, MTsNMO, M., 2011, 136 pp.

[20] A. Blass, G. Exoo, F. Harary, “Paley graphs satisfy all first-order adjacency axioms”, J. Graph Theory, 5:4 (1981), 435–439 | DOI | MR | Zbl