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Volumn 206, Issue 10, 2015, Pages 1340-1374

Independence numbers and chromatic numbers of the random subgraphs of some distance graphs

Author keywords

Chromatic number; Distance graph; Independence number; Random graph

Indexed keywords


EID: 84953283845     PISSN: 10645616     EISSN: 14684802     Source Type: Journal    
DOI: 10.1070/SM2015v206n10ABEH004498     Document Type: Article
Times cited : (31)

References (66)
  • 2
    • 84931084539 scopus 로고
    • A certain constructive estimate of the Ramsey number
    • Z. Nagy, "A certain constructive estimate of the Ramsey number", Mat. Lapok 23(1972) (1974), 301-302.
    • (1974) Mat. Lapok , vol.23 , Issue.1972 , pp. 301-302
    • Nagy, Z.1
  • 3
    • 0003792618 scopus 로고
    • 2nd ed., Wiley-Intersci. Ser. Discrete Math. Optim., John Wiley & Sons, Inc., New York
    • R. L. Graham, B. L. Rothschild and J. H. Spencer, Ramsey theory, 2nd ed., Wiley-Intersci. Ser. Discrete Math. Optim., John Wiley & Sons, Inc., New York 1990, xii+196 pp.
    • (1990) Ramsey theory
    • Graham, R.L.1    Rothschild, B.L.2    Spencer, J.H.3
  • 4
    • 85164076623 scopus 로고    scopus 로고
    • 3rd ed., Moscow Center for Continuous Mathematical Education, Moscow
    • A. M. Raigorodskii, Probability and algebra in combinatorics, 3rd ed., Moscow Center for Continuous Mathematical Education, Moscow 2015, 48 pp. (Russian)
    • (2015) Probability and Algebra in Combinatorics , pp. 48
    • Raigorodskii, A.M.1
  • 5
    • 84976175804 scopus 로고
    • The realization of distances within sets in Euclidean space
    • D. G. Larman and C. A. Rogers, "The realization of distances within sets in Euclidean space", Mathematika 19:1 (1972), 1-24.
    • (1972) Mathematika , vol.19 , Issue.1 , pp. 1-24
    • Larman, D.G.1    Rogers, C.A.2
  • 7
    • 85018485710 scopus 로고    scopus 로고
    • Borsuks problem and the chromatic numbers of some metric spaces
    • 1
    • A. M. Raigorodskii, "Borsuks problem and the chromatic numbers of some metric spaces", Uspekhi Mat. Nauk 56:1(337) (2001), 107-146;
    • (2001) Uspekhi Mat. Nauk , vol.56 , Issue.337 , pp. 107-146
    • Raigorodskii, A.M.1
  • 8
    • 0041082751 scopus 로고    scopus 로고
    • English transl.
    • English transl. in Russian Math. Surveys 56:1 (2001), 103-139.
    • (2001) Russian Math. Surveys , vol.56 , Issue.1 , pp. 103-139
  • 9
    • 84898002428 scopus 로고    scopus 로고
    • Coloring distance graphs and graphs of diameters
    • Springer, New York
    • A. M. Raigorodskii, "Coloring distance graphs and graphs of diameters", Thirty essays on geometric graph theory, Springer, New York 2013, pp. 429-460.
    • (2013) Thirty Essays on Geometric Graph Theory , pp. 429-460
    • Raigorodskii, A.M.1
  • 10
    • 36049022123 scopus 로고    scopus 로고
    • Moscow Center for Continuous Mathematical Education, Moscow (Russian
    • A. M. Raigorodskii, Linear-algebraic method in combinatorics, Moscow Center for Continuous Mathematical Education, Moscow 2015, 136 pp. (Russian)
    • (2015) Linear-Algebraic Method in Combinatorics , pp. 136
    • Raigorodskii, A.M.1
  • 11
    • 0004018188 scopus 로고
    • Wiley-Intersci. Ser. Discrete Math. Optim., John Wiley & Sons, Inc., New York
    • P. K. Agarwal and J. Pach, Combinatorial geometry, Wiley-Intersci. Ser. Discrete Math. Optim., John Wiley & Sons, Inc., New York 1995, xiv+354 pp.
    • (1995) Combinatorial geometry
    • Agarwal, P.K.1    Pach, J.2
  • 12
    • 24544463963 scopus 로고    scopus 로고
    • Erdõs on unit distances and the Szemeredi-Trotter theorems
    • Budapest
    • L. A. Szekely, "Erdõs on unit distances and the Szemeredi-Trotter theorems", Paul Erdõs and his mathematics, vol. II (Budapest 1999
    • (1999) Paul Erdõs and his Mathematics , vol.2
    • Szekely, L.A.1
  • 13
    • 24544463963 scopus 로고    scopus 로고
    • Janos Bolyai Math. Soc., Budapest
    • Bolyai Soc. Math. Stud., vol. 11, Janos Bolyai Math. Soc., Budapest 2002, pp. 649-666.
    • (2002) Bolyai Soc. Math. Stud. , vol.11 , pp. 649-666
  • 15
    • 0003532728 scopus 로고
    • Old and new unsolved problems in plane geometry and number theory
    • Math. Assoc. America, Washington, DC
    • V. Klee and S. Wagon, Old and new unsolved problems in plane geometry and number theory, Dolciani Math. Exp., vol. 11, Math. Assoc. America, Washington, DC 1991, xvi+333 pp.
    • (1991) Dolciani Math. Exp. , vol.11
    • Klee, V.1    Wagon, S.2
  • 18
  • 19
    • 84874571605 scopus 로고    scopus 로고
    • Moscow Center for Continuous Mathematical Education, Moscow. (Russian
    • A. M. Raigorodskii, Models of random graphs, Moscow Center for Continuous Mathematical Education, Moscow 2011, 136 pp. (Russian)
    • (2011) Models of Random Graphs , pp. 136
    • Raigorodskii, A.M.1
  • 20
    • 1642373920 scopus 로고    scopus 로고
    • 2nd ed., Cambridge Stud. Adv. Math., Cambridge Univ. Press, Cambridge
    • B. Bollobas, Random graphs, 2nd ed., Cambridge Stud. Adv. Math., vol. 73, Cambridge Univ. Press, Cambridge 2001, xviii+498 pp.
    • (2001) Random Graphs , vol.73
    • Bollobas, B.1
  • 21
    • 0005685497 scopus 로고    scopus 로고
    • 2nd ed., Fizmatlit, Moscow
    • V. F. Kolchin, Random graphs, 2nd ed., Fizmatlit, Moscow 2004, 256 pp.;
    • (2004) Random Graphs , pp. 256
    • Kolchin, V.F.1
  • 22
    • 0003371188 scopus 로고    scopus 로고
    • English transl. of 1st ed., Cambridge Univ. Press, Cambridge
    • English transl. of 1st ed., Encyclopedia Math. Appl., vol. 53, Cambridge Univ. Press, Cambridge 1999, xii+252 pp.
    • (1999) Encyclopedia Math. Appl. , vol.53
  • 23
    • 0003616602 scopus 로고    scopus 로고
    • Wiley-Intersci. Ser. Discrete Math. Optim., Wiley-Interscience, New York
    • S. Janson, T. Luczak and A. Rucinski, Random graphs, Wiley-Intersci. Ser. Discrete Math. Optim., Wiley-Interscience, New York 2000, xii+333 pp.
    • (2000) Random Graphs
    • Janson, S.1    Luczak, T.2    Rucinski, A.3
  • 24
    • 0002909354 scopus 로고
    • The chromatic number of random graphs
    • B. Bollobas, "The chromatic number of random graphs", Combinatorica 8:1 (1988), 49-55.
    • (1988) Combinatorica , vol.8 , Issue.1 , pp. 49-55
    • Bollobas, B.1
  • 25
    • 34249925281 scopus 로고
    • The chromatic number of random graphs
    • T. Luczak, "The chromatic number of random graphs", Combinatorica 11:1 (1991), 45-54.
    • (1991) Combinatorica , vol.11 , Issue.1 , pp. 45-54
    • Luczak, T.1
  • 26
    • 85164071480 scopus 로고
    • On the independence number of random subgraphs of the n-cube
    • Poznan
    • K. Weber, "On the independence number of random subgraphs of the n-cube", Random graphs 85 (Poznan 1985
    • (1985) Random Graphs 85
    • Weber, K.1
  • 27
    • 77957322910 scopus 로고
    • Ann. Discrete Math. 33, North-Holland, Amsterdam
    • North-Holland Math. Stud., vol. 144, Ann. Discrete Math., 33, North-Holland, Amsterdam 1987, pp. 333-337.
    • (1987) North-Holland Math. Stud. , vol.144 , pp. 333-337
  • 29
    • 0003780715 scopus 로고
    • Addison-Wesley Publishing Co., Reading, Mass.-Menlo Park, Calif.-London
    • F. Harary, Graph theory, Addison-Wesley Publishing Co., Reading, Mass.-Menlo Park, Calif.-London 1969, ix+274 pp.
    • (1969) Graph Theory
    • Harary, F.1
  • 30
    • 0003430191 scopus 로고    scopus 로고
    • 2nd ed. Wiley-Intersci. Ser. Discrete Math. Optim., Wiley-Interscience [John Wiley & Sons], New York
    • N. Alon and J. H. Spencer, The probabilistic method, 2nd ed., Wiley-Intersci. Ser. Discrete Math. Optim., Wiley-Interscience [John Wiley & Sons], New York 2000, xviii+301 pp.
    • (2000) The Probabilistic Method
    • Alon, N.1    Spencer, J.H.2
  • 31
    • 51249183723 scopus 로고
    • A note on the realization of distances within sets in Euclidean space
    • D. G. Larman, "A note on the realization of distances within sets in Euclidean space", Comment. Math. Helv. 53:4 (1978), 529-535.
    • (1978) Comment. Math. Helv. , vol.53 , Issue.4 , pp. 529-535
    • Larman, D.G.1
  • 32
    • 51249185135 scopus 로고
    • Intersection theorems with geometric consequences
    • P. Frankl and R. M. Wilson, "Intersection theorems with geometric consequences", Combinatorica 1:4 (1981), 357-368.
    • (1981) Combinatorica , vol.1 , Issue.4 , pp. 357-368
    • Frankl, P.1    Wilson, R.M.2
  • 34
    • 77950006360 scopus 로고    scopus 로고
    • Three lectures on the Borsuk partition problem
    • London Math. Soc. Lecture Note Ser., Cambridge Univ. Press, Cambridge
    • A. M. Raigorodskii, "Three lectures on the Borsuk partition problem", Surveys in contemporary mathematics, London Math. Soc. Lecture Note Ser., vol. 347, Cambridge Univ. Press, Cambridge 2008, pp. 202-247.
    • (2008) Surveys in contemporary mathematics , vol.347 , pp. 202-247
    • Raigorodskii, A.M.1
  • 35
    • 54849423868 scopus 로고    scopus 로고
    • Around Borsuks hypo thesis
    • Rossiiskii Universitet Druzhby Narodov, Moscow 2007
    • A. M. Raigorodskii, "Around Borsuks hypothesis", Geometry and mechanics, Sovrem. Mat. Fundam. Napravl., vol. 23, Rossiiskii Universitet Druzhby Narodov, Moscow 2007, pp. 147-164;
    • Geometry and Mechanics, Sovrem. Mat. Fundam. Napravl. , vol.23 , pp. 147-164
    • Raigorodskii, A.M.1
  • 36
    • 54849423868 scopus 로고    scopus 로고
    • English transl.
    • English transl. in J. Math. Sci. (N. Y.) 154:4 (2008), 604-623.
    • (2008) J. Math. Sci. (N. Y. , vol.154 , Issue.4 , pp. 604-623
  • 37
    • 33645455244 scopus 로고    scopus 로고
    • The problems of Borsuk and Grunbaum on lattice polytopes
    • A. M. Raigorodskii, "The problems of Borsuk and Grunbaum on lattice polytopes", Izv. Ross. Akad. Nauk Ser. Mat. 69:3 (2005), 81-108;
    • (2005) Izv. Ross. Akad. Nauk Ser. Mat. , vol.69 , Issue.3 , pp. 81-108
    • Raigorodskii, A.M.1
  • 38
    • 33645455244 scopus 로고    scopus 로고
    • English transl.
    • English transl. in Izv. Math. 69:3 (2005), 513-537.
    • (2005) Izv. Math. , vol.69 , Issue.3 , pp. 513-537
  • 39
    • 18944367235 scopus 로고    scopus 로고
    • The Erdõs-Hadwiger problem and the chromatic numbers of finite geometric graphs
    • A. M. Raigorodskii, "The Erdõs-Hadwiger problem and the chromatic numbers of finite geometric graphs", Mat. Sb. 196:1 (2005), 123-156;
    • (2005) Mat. Sb. , vol.196 , Issue.1 , pp. 123-156
    • Raigorodskii, A.M.1
  • 40
    • 18944367235 scopus 로고    scopus 로고
    • English transl.
    • English transl. in Sb. Math. 196:1 (2005), 115-146.
    • (2005) Sb. Math. , vol.196 , Issue.1 , pp. 115-146
  • 41
    • 84874578124 scopus 로고    scopus 로고
    • On independence numbers of distance graphs with vertices in {-1, 0, 1}n: Estimates, conjectures, and applications to the Nelson-Erdõs-Hadwiger problem and the Borsuk problem
    • VINITI, Moscow
    • A. E. Guterman, V. K. Lyubimov, A. M. Raigorodskii and S. A. Usachev, "On independence numbers of distance graphs with vertices in {-1, 0, 1}n: Estimates, conjectures, and applications to the Nelson-Erdõs-Hadwiger problem and the Borsuk problem", Sovrem. Mat. Prilozh., vol. 65, VINITI, Moscow 2009, pp. 82-100;
    • (2009) Sovrem. Mat. Prilozh. , vol.65 , pp. 82-100
    • Guterman, A.E.1    Lyubimov, V.K.2    Raigorodskii, A.M.3    Usachev, S.A.4
  • 42
    • 77949303516 scopus 로고    scopus 로고
    • English transl.
    • English transl. in J. Math. Sci. (N. Y.) 165:6 (2010), 689-709.
    • (2010) J. Math. Sci. (N. Y. , vol.165 , Issue.6 , pp. 689-709
  • 43
    • 84862136768 scopus 로고    scopus 로고
    • On the chromatic numbers of spheres in Rn
    • A. M. Raigorodskii, "On the chromatic numbers of spheres in Rn", Combinatorica 32:1 (2012), 111-123.
    • (2012) Combinatorica , vol.32 , Issue.1 , pp. 111-123
    • Raigorodskii, A.M.1
  • 44
    • 84953319181 scopus 로고    scopus 로고
    • Counterexamples to Borsuks conjecture on spheres of small radii
    • A. Raigorodskii and A. Kupavskii, "Counterexamples to Borsuks conjecture on spheres of small radii", Moscow J. Combin. Number Theory 2:4 (2012), 27-48.
    • (2012) Moscow J. Combin. Number Theory , vol.2 , Issue.4 , pp. 27-48
    • Raigorodskii, A.1    Kupavskii, A.2
  • 45
    • 84898811812 scopus 로고    scopus 로고
    • An improvement of the Frankl-Wilson theorem on the number of edges in a hypergraph with forbidden intersections of edges
    • E. I. Ponomarenko and A. M. Raigorodskii, "An improvement of the Frankl-Wilson theorem on the number of edges in a hypergraph with forbidden intersections of edges", Dokl. Ross. Akad. Nauk 454:3 (2014), 268-269;
    • (2014) Dokl. Ross. Akad. Nauk , vol.454 , Issue.3 , pp. 268-269
    • Ponomarenko, E.I.1    Raigorodskii, A.M.2
  • 46
    • 85164087220 scopus 로고    scopus 로고
    • English transl.
    • English transl. in Dokl. Math. 89:1 (2014), 59-60.
    • (2014) Dokl. Math. , vol.89 , Issue.1 , pp. 59-60
  • 47
    • 84897971375 scopus 로고    scopus 로고
    • New estimates in the problem of the number of edges in a hypergraph with forbidden intersections
    • E. I. Ponomarenko and A. M. Raigorodskii, "New estimates in the problem of the number of edges in a hypergraph with forbidden intersections", Problemy Peredachi Informatsii 49:4 (2013), 98-104;
    • (2013) Problemy Peredachi Informatsii , vol.49 , Issue.4 , pp. 98-104
    • Ponomarenko, E.I.1    Raigorodskii, A.M.2
  • 48
    • 84897971375 scopus 로고    scopus 로고
    • English transl.
    • English transl. in Problems Inform. Transmission 49:4 (2013), 384-390.
    • (2013) Problems Inform. Transmission , vol.49 , Issue.4 , pp. 384-390
  • 49
    • 0004074813 scopus 로고
    • Blaisdell Publishing Co., Waltham, Mass.-Toronto, Ont.-London
    • M. Hall, Jr., Combinatorial theory, Blaisdell Publishing Co., Waltham, Mass.-Toronto, Ont.-London 1967, x+310 pp.
    • (1967) Combinatorial Theory
    • Hall, M.1
  • 51
    • 0003115446 scopus 로고
    • On a packing and covering problem
    • V. Rõdl, "On a packing and covering problem", European J. Combin. 6:1 (1985), 69-78.
    • (1985) European J. Combin. , vol.6 , Issue.1 , pp. 69-78
    • Rõdl, V.1
  • 52
    • 9244251798 scopus 로고    scopus 로고
    • Lectures on topological methods in combinatorics and geometry, Universitext, Springer, Berlin
    • J. Matousek, Using the Borsuk-Ulam theorem, Lectures on topological methods in combinatorics and geometry, Universitext, Springer, Berlin 2003, xii+196 pp.
    • (2003) Using the Borsuk-Ulam theorem
    • Matousek, J.1
  • 53
    • 84960611591 scopus 로고
    • Intersection theorems for systems of finite sets
    • P. Erdõs, Chao Ko and R. Rado, "Intersection theorems for systems of finite sets", Quart. J. Math. Oxford Ser. (2) 12:1 (1961), 313-320.
    • (1961) Quart. J. Math. Oxford Ser. , vol.12 , Issue.1 , pp. 313-320
    • Erdõs, P.1    Chao, Ko.2    Rado, R.3
  • 56
    • 0002877406 scopus 로고
    • On the factorization of the complete uniform hypergraph
    • Colloq., dedicated to P. Erdõs on his 60th birthday (Keszthely
    • Zs. Baranyai, "On the factorization of the complete uniform hypergraph", Infinite and finite sets, vol. I, Colloq., dedicated to P. Erdõs on his 60th birthday (Keszthely 1973
    • (1973) Infinite and Finite Sets , vol.1
    • Baranyai, Z.1
  • 57
    • 85164087145 scopus 로고
    • North-Holland, Amsterdam
    • Colloq. Math. Soc. Janos Bolyai, vol. 10, North-Holland, Amsterdam 1973, pp. 91-108.
    • (1973) Colloq. Math. Soc. Janos Bolyai , vol.10 , pp. 91-108
  • 58
    • 0000059891 scopus 로고    scopus 로고
    • The Borsuk problem for (0, 1)-polyhedra and cross polytopes
    • A. M. Raigorodskii, "The Borsuk problem for (0, 1)-polyhedra and cross polytopes", Dokl. Ross. Akad. Nauk 371:5 (2000), 600-603;
    • (2000) Dokl. Ross. Akad. Nauk , vol.371 , Issue.5 , pp. 600-603
    • Raigorodskii, A.M.1
  • 59
    • 0012897959 scopus 로고    scopus 로고
    • English transl.
    • English transl. in Dokl. Math. 61 (2000), 256-259.
    • (2000) Dokl. Math. , vol.61 , pp. 256-259
  • 60
    • 0036422050 scopus 로고    scopus 로고
    • Borsuks problem for (0, 1)-polytopes and cross-polytopes
    • A. M. Raigorodskii, "Borsuks problem for (0, 1)-polytopes and cross-polytopes", Dokl. Ross. Akad. Nauk 384:5 (2002), 593-597;
    • (2002) Dokl. Ross. Akad. Nauk , vol.384 , Issue.5 , pp. 593-597
    • Raigorodskii, A.M.1
  • 61
    • 0036579396 scopus 로고    scopus 로고
    • English transl.
    • English transl. in Dokl. Math. 65:3 (2002), 413-416.
    • (2002) Dokl. Math. , vol.65 , Issue.3 , pp. 413-416
  • 62
    • 0345548662 scopus 로고    scopus 로고
    • The problem of Borsuk, Hadwiger, and Grunbaum for some classes of polytopes and graphs
    • A. M. Raigorodskii, "The problem of Borsuk, Hadwiger, and Grunbaum for some classes of polytopes and graphs", Dokl. Ross. Akad. Nauk 388:6 (2003), 738-742;
    • (2003) Dokl. Ross. Akad. Nauk , vol.388 , Issue.6 , pp. 738-742
    • Raigorodskii, A.M.1
  • 63
    • 27444440011 scopus 로고    scopus 로고
    • English transl.
    • English transl. in Dokl. Math. 67:1 (2003), 85-89.
    • (2003) Dokl. Math. , vol.67 , Issue.1 , pp. 85-89
  • 64
    • 84855967578 scopus 로고    scopus 로고
    • On the Ramsey numbers for complete distance graphs with vertices in {0, 1}n
    • K. A. Mikhailov and A. M. Raigorodskii, "On the Ramsey numbers for complete distance graphs with vertices in {0, 1}n", Mat. Sb. 200:12 (2009), 63-80;
    • (2009) Mat. Sb. , vol.200 , Issue.12 , pp. 63-80
    • Mikhailov, K.A.1    Raigorodskii, A.M.2
  • 65
    • 77149165996 scopus 로고    scopus 로고
    • English transl.
    • English transl. in Sb. Math. 200:12 (2009), 1789-1806.
    • (2009) Sb. Math. , vol.200 , Issue.12 , pp. 1789-1806
  • 66
    • 0001086798 scopus 로고
    • A combinatorial problem in geometry
    • P. Erdõs and G. Szekeres, "A combinatorial problem in geometry", Compositio Math. 2 (1935), 463-470.
    • (1935) Compositio Math. , vol.2 , pp. 463-470
    • Erdõs, P.1    Szekeres, G.2


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