Geodesic
On the Ramsey numbers for complete distance graphs with vertices in $\{0,1\}^n$
Sbornik. Mathematics, Tome 200 (2009) no. 12, pp. 1789-1806 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

A new problem of Ramsey type is posed for complete distance graphs in $\mathbb R^n$ with vertices in the Boolean cube. This problem is closely related to the classical Nelson-Erdős-Hadwiger problem on the chromatic number of a space. Several quite sharp estimates are obtained for certain numerical characteristics that appear in the framework of the problem. Bibliography: 15 titles.
Keywords: Ramsey numbers, distance graphs, chromatic number. 
@article{SM_2009_200_12_a2,
     author = {K. A. Mikhailov and A. M. Raigorodskii},
     title = {On the {Ramsey} numbers for complete distance graphs with vertices in~$\{0,1\}^n$},
     journal = {Sbornik. Mathematics},
     pages = {1789--1806},
     year = {2009},
     volume = {200},
     number = {12},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2009_200_12_a2/}
}
TY  - JOUR
AU  - K. A. Mikhailov
AU  - A. M. Raigorodskii
TI  - On the Ramsey numbers for complete distance graphs with vertices in $\{0,1\}^n$
JO  - Sbornik. Mathematics
PY  - 2009
SP  - 1789
EP  - 1806
VL  - 200
IS  - 12
UR  - http://geodesic.mathdoc.fr/item/SM_2009_200_12_a2/
LA  - en
ID  - SM_2009_200_12_a2
ER  - 
%0 Journal Article
%A K. A. Mikhailov
%A A. M. Raigorodskii
%T On the Ramsey numbers for complete distance graphs with vertices in $\{0,1\}^n$
%J Sbornik. Mathematics
%D 2009
%P 1789-1806
%V 200
%N 12
%U http://geodesic.mathdoc.fr/item/SM_2009_200_12_a2/
%G en
%F SM_2009_200_12_a2
K. A. Mikhailov; A. M. Raigorodskii. On the Ramsey numbers for complete distance graphs with vertices in $\{0,1\}^n$. Sbornik. Mathematics, Tome 200 (2009) no. 12, pp. 1789-1806. http://geodesic.mathdoc.fr/item/SM_2009_200_12_a2/

[1] F. Harary, Graph theory, Addison-Wesley, Reading, MA–Menlo Park, CA–London, 1969 | MR | MR | Zbl | Zbl

[2] M. Hall, jr., Combinatorial theory, Blaisdell, Waltham, MA–Toronto, ON–London, 1967 | MR | MR | Zbl | Zbl

[3] R. L. Graham, Rudiments of Ramsey theory, CBMS Regional Conf. Ser. in Math., 45, Amer. Math. Soc., Providence, RI, 1981 | MR | MR | Zbl | Zbl

[4] R. L. Graham, B. L. Rothschild, J. H. Spencer, Ramsey theory, Wiley-Intersci. Ser. Discrete Math. Optim., Wiley, New York, 1990 | MR | Zbl

[5] A. M. Raigorodskii, Lineino-algebraicheskii metod v kombinatorike, MTsNMO, Moskva, 2007

[6] N. G. de Bruijn, P. Erdős, “A colour problem for infinite graphs and a problem in the theory of relations”, Nederl. Akad. Wetensch. Proc. Ser. A, 54:5 (1951), 371–373 | MR | Zbl

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

[8] A. M. Raigorodskii, “Some problems in combinatorial geometry, and the linear algebra method in combinatorics”, Chebyshëvskii sbornik, 7, no. 3, 2006, 168–189 | MR

[9] P. Brass, W. Moser, J. Pach, Research problems in discrete geometry, Springer-Verlag, New York, 2005 | MR | Zbl

[10] K. Prachar, Primzahlverteilung, Grundlehren Math. Wiss., 91, Springer-Verlag, Berlin–Göttingen–Heidelberg, 1957 | MR | MR | Zbl | Zbl

[11] P. Frankl, R. M. Wilson, “Intersection theorems with geometric consequences”, Combinatorica, 1:4 (1981), 357–368 | DOI | MR | Zbl

[12] N. Alon, J. H. Spencer, The probabilistic method, Wiley-Intersci. Ser. Discrete Math. Optim., Wiley, New York, 2000 | MR | Zbl

[13] B. Bollobás, Random graphs, Cambridge Stud. Adv. Math., 73, Cambridge Univ. Press, Cambridge, 2001 | MR | Zbl

[14] A. M. Raigorodskii, Veroyatnost i algebra v kombinatorike, MTsNMO, M., 2008

[15] P. Frankl, R. Rödl, “Forbidden intersections”, Trans. Amer. Math. Soc., 300:1 (1987), 259–286 | DOI | MR | Zbl