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Embeddability of finite distance graphs with a large chromatic number in random graphs. (English. Russian original) Zbl 1194.05026
Dokl. Math. 77, No. 1, 13-16 (2008); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 418, No. 1, 19-22 (2008).

MSC:
05C10 Planar graphs; geometric and topological aspects of graph theory
05C80 Random graphs (graph-theoretic aspects)
05C15 Coloring of graphs and hypergraphs
05C12 Distance in graphs
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References:
[1] F. Harary, Graph Theory (Addison-Wesley, Reading, Mass., 1969; Mir, Moscow, 1973).
[2] N. G. De Bruijn and P. Erdös, Proc. Koninkl. Nederl. Acad. Wet. Ser. A 54, 371–373 (1951).
[3] A. M. Raigorodskii, Usp. Mat. Nauk 56(1), 107–146 (2001). · doi:10.4213/rm358
[4] P. Brass, W. Moser, and J. Pach, Research Problems in Discrete Geometry (Springer-Verlag, Berlin, 2005).
[5] L. Moser and W. Moser, Canad. Math. Bull. 4, 187–189 (1961).
[6] H. Hadwiger, Elem. Math. 16, 103–104 (1961).
[7] O. Nechushtan, Discrete Math. 256, 499–507 (2002). · Zbl 1009.05058 · doi:10.1016/S0012-365X(00)00406-4
[8] D. Coulson, Discrete Math. 256, 83–90 (2002). · Zbl 1007.05052 · doi:10.1016/S0012-365X(01)00183-2
[9] L. L. Ivanov, Usp. Mat. Nauk 61, 371 (2006).
[10] D. G. Larman and C. A. Rogers, Mathematika 19, 1–24 (1972). · Zbl 0246.05020 · doi:10.1112/S0025579300004903
[11] A. M. Raigorodskii, Dokl. Math. 72, 516–518 (2005) [Dokl. Akad. Nauk 403, 169–171 (2005)].
[12] A. M. Raigorodskii, Fundam. Prikl. Mat. 11(6), 131–141 (2005).
[13] A. M. Raigorodskii, Usp. Mat. Nauk 61(4), 195–196 (2006). · doi:10.4213/rm1696
[14] B. Bollobàs, Random Graphs (Cambridge Univ. Press, Cambridge, 2001).
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