Independence numbers of random subgraphs of a distance graph

Mathematical Notes

Volumn 99, Issue 1-2, 2016, Pages 312-319

  Pyaderkin, M M ^a  

^a MOSCOW STATE UNIVERSITY   (Russian Federation)

Author keywords

distance graph; Erd s R nyi model; independence number; random subgraph

Indexed keywords

EID: 84962407595     PISSN: 00014346     EISSN: None     Source Type: Journal    
DOI: 10.1134/S000143461601034X     Document Type: Article

References (24)

1. A. M. Raigorodskii, “Cliques and cycles in distance graphs and graphs of diameters,” in Contemp. Math., Vol. 625: Discrete Geometry and Algebraic Combinatorics (Amer. Math. Soc., Providence, RI, 2014), pp. 93–109.
2. A. M. Raigorodskii, “Coloring distance graphs and graphs of diameters,” in Thirty Essays on Geometric Graph Theory Springer, New York, (2013), pp. 429–460.
3. A. M. Raigorodskii, “Borsuk’s problem and the chromatic numbers of some metric spaces,” Uspekhi Mat. Nauk 56 (1), 107–146 (2001) [RussianMath. Surveys 56 (1), 103–139 (2001)].
4. A. M. Raigorodskii, “On the chromatic numbers of spheres in Euclidean spaces,” Dokl. Ross. Akad. Nauk 432 (2), 174–177 (2010) [Dokl.Math. 81 (3), 379–382 (2010)].
5. A. M. Raigorodskii, “On the chromatic numbers of spheres in Rn,” Combinatorica 32 (1), 111–123 (2012).
6. J. Balogh, A. Kostochka, and A. Raigorodskii, “Coloring some finite sets in Rn,” Discuss. Math. Graph Theory 33 (1), 25–31 (2013).
7. J. Pach and P. K. Agarwal, Combinatorial Geometry (John Wiley & Sons, New York, 1995).
8. L. A. Székely, “Erdos on unit distances and the Szemerédi–Trotter theorems,” in Bolyai Soc. Math. Stud., Vol. 11: Paul Erdos and HisMathematics, II János Bolyai Math. Soc., Budapest, (2002), pp. 649–666.
9. A. Soifer, The Mathematical Coloring Book: Mathematics of Coloring and the Colorful Life of Its Creators (Springer, New York, 2009).
10. V. Klee and S. Wagon, Old and New Unsolved Problems in Plane Geometry and Number Theory, Vol. 11 in DolcianiMath. Exp. (Math. Assoc. America, Washington, DC, 1991).
11. V. Boltyanski, H. Martini, and P. S. Soltan, Excursions into Combinatorial Geometry (Springer-Verlag, Berlin, 1997).
12. A. M. Raigorodskii, “Three lectures on the Borsuk partition problem,” in London Math. Soc. Lecture Note Ser., Vol. 347: Surveys in Contemporary Mathematics Cambridge Univ. Press, Cambridge, (2007), pp. 202–248.
13. A. M. Raigorodskii, “Around Borsuk’s hypothesis,” in Sovrem. Mat., Fundam. Napravl., Vol. 23: Geometriya i Mekhanika Peoples’ Friendship University of Russia, Moscow, (2007), pp. 147–164. [J. Math. Sci., New York 154 (4), 604–623 (2008)].
14. R. L. Graham, B. L. Rothschild, and J. H. Spencer, Ramsey Theory (John Wiley & Sons, New York, 1990).
15. Z. Nagy, “A certain constructive estimate of the Ramsey number,” Mat. Lapok 23, 301–302 (1974).
16. F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes. I (North-Holland, Amsterdam–New York–Oxford, 1977).
17. L. Bassalygo, G. Cohen, and G. Zémor, “Codes with forbidden distances,” Discrete Math. 213 (1–3), 3–11 (2000).
18. B. Bollobás, Random Graphs (Cambridge Univ. Press, Cambridge, 2001).
19. S. Janson, T. Luczak, and A. Rucinski, Random Graphs (Wiley-Interscience, New York, 2000).
20. V. F. Kolchin, Random Graphs (Fizmatlit, Moscow, 2000) [in Russian].
21. L. I. Bogolyubskii, A. S. Gusev, M. M. Pyaderkin, and A. M. Raigorodskii, “Independence numbers and chromatic numbers of random subgraphs in some sequences of graphs,” Dokl. Ross. Akad. Nauk 457 (4), 383–387 (2014) [Dokl.Math. 90 (1), 462–465 (2014)].
22. L. I. Bogolyubskii, A. S. Gusev, M. M. Pyaderkin, and A. M. Raigorodskii, “Independence numbers and chromatic numbers of the random subgraphs of some distance graphs,” Mat. Sb. 206 (10), 3–36 (2015) [Sb. Math. 206 (10), 1340–1374 (2015)].
23. E. E. Demekhin, A. M. Raigorodskii, and O. I. Rubanov, “Distance graphs having large chromatic numbers and containing no cliques or cycles of a given size,” Mat. Sb. 204 (4), 49–78 (2013) [Sb. Math. 204 (4), 508–538 (2013)].
24. A. M. Raigorodskii and K. A. Mikhailov, “On the Ramsey numbers for complete distance graphs with vertices in 0, 1n,” Mat. Sb. 200 (12), 63–80 (2009) [Sb.Math. 200 (12), 1789–18706 (2009)].