@article{TVP_2015_60_3_a1,
author = {A. V. Burkin},
title = {Small subgraphs in random distance graphs},
journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
pages = {439--458},
year = {2015},
volume = {60},
number = {3},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TVP_2015_60_3_a1/}
}
A. V. Burkin. Small subgraphs in random distance graphs. Teoriâ veroâtnostej i ee primeneniâ, Tome 60 (2015) no. 3, pp. 439-458. http://geodesic.mathdoc.fr/item/TVP_2015_60_3_a1/
[1] Erd{ő}s P., Rényi A., “On the evolution of random graphs”, Publ. Math. Inst. Hung. Acad. Sci., 5 (1960), 17–61 | MR | Zbl
[2] Bollobás B., Random Graphs, Cambridge Stud. Adv. Math., 73, Cambridge Univ. Press, Cambridge, 2001, 528 pp. | Zbl
[3] Janson S., Łuczak T., Ruciński A., Random Graphs, Wiley, New York, 2000, 333 pp. | MR | Zbl
[4] Raigorodskii A. M., Modeli sluchainykh grafov, MTsNMO, M., 2011, 136 pp.
[5] Kolchin V. F., Sluchainye grafy, Fizmatlit, M., 2000, 255 pp. | MR
[6] Bollobás B., “Threshold functions for small subgraphs”, Math. Proc. Cambridge Philos. Soc., 90:2 (1981), 197–206 | DOI | MR | Zbl
[7] Ruciński A., Vince A., “Balanced graphs and the problem of subgraphs of random graphs”, Proceedings of the Sixteenth {S}outheastern International Conference on Combinatorics, Graph Theory and Computing, Congr. Numer., 49, Utilitas Math., Winnipeg, 1985, 181–190 | MR
[8] Raigorodskii A. M., “Problema Borsuka dlya (0,1)-mnogogrannikov i kross-politopov”, Dokl. RAN, 371:5 (2000), 593–597 | MR
[9] Raigorodskii A. M., “Problema Borsuka i khromaticheskie chisla nekotorykh metricheskikh prostranstv”, Uspekhi matem. nauk, 56:1 (2001), 107–146 | DOI | MR | Zbl
[10] Raigorodskii A. M., “Problema Borsuka dlya tselochislennykh mnogogrannikov”, Matem. sb., 193:10 (2002), 139–160 | DOI | MR | Zbl
[11] Raigorodskii A. M., “Problema Erdesha–Khadvigera i khromaticheskie chisla konechnykh geometricheskikh grafov”, Matem. sb., 196:1 (2005), 123–156 | DOI | MR | Zbl
[12] Raigorodskii A. M., “Problemy Borsuka i Gryunbauma dlya reshetchatykh mnogogrannikov”, Izv. RAN. Ser. matem., 69:3 (2005), 81–108 | DOI | MR | Zbl
[13] Raigorodskii A. M., Lineino-algebraicheskii metod v kombinatorike, MTsNMO, M., 2007, 136 pp.
[14] Raigorodskii A. M., “Three lectures on the Borsuk partition problem”, Surveys in Contemporary Mathematics, Ed. by N. Young et al., Cambridge Univ. Press, Cambridge, 2007, 202–247 | DOI | MR
[15] Raigorodskii A. M., “Around Borsuk's conjecture”, J. Math. Sci., 154:4 (2008), 604–623 | DOI | MR | Zbl
[16] Raigorodskii A. M., “Coloring distance graphs and graphs of diameters”, Thirty Essays on Geometric Graph Theory, Springer, Berlin, 2013, 429–460 | DOI | MR | Zbl
[17] Raigorodskii A. M., “On the chromatic numbers of spheres in $\mathbb R^n$”, Combinatorica, 32:1 (2012), 111–123 | DOI | MR | Zbl
[18] Zhukovskii M. E., “O veroyatnosti vkhozhdeniya kopii fiksirovannogo grafa v sluchainyi distantsionnyi graf”, Matem. zametki, 92:6 (2012), 844–855 | DOI | MR | Zbl
[19] Kharari F., Teoriya grafov, Editorial URSS, M., 2003, 300 pp.
[20] Łuczak T., Pittel B., Wierman J. C., “The structure of a random graph at the point of the phase transition”, Trans. Amer. Math. Soc., 341:2 (1994), 721–748 | DOI | MR
[21] Frieze A., Krivelevich M., “On the non-planarity of a random subgraph”, Combin. Probab. Comput., 22:5 (2013), 722–732 | DOI | MR | Zbl
[22] Whitney H., “Non-separable and planar graphs”, Trans. Amer. Math. Soc., 34:2 (1932), 339–362 | DOI | MR
[23] Yarmukhametov A. R., “O svyaznosti sluchainykh distantsionnykh grafov spetsialnogo vida”, Chebyshevskii sb., 10:1 (2009), 95–108 | MR
[24] Alon N., Spenser Dzh., Veroyatnostnyi metod, BINOM, M., 2007, 320 pp.
[25] Karp R. M., “The transitive closure of a random digraph”, Random Structures Algorithms, 1:1 (1990), 73–93 | DOI | MR | Zbl