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New Turán Type Bounds for Johnson Graphs

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Abstract

We obtain a new bound on the number of edges in induced subgraphs of Johnson graphs.

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References

  1. Raigorodskii, A.M., Cliques and Cycles in Distance Graphs and Graphs of Diameters, Discrete Geometry and Algebraic Combinatorics (AMS Special Session on Discrete Geometry and Algebraic Combinatorics, San Diego, CA, USA, Jan. 11, 2013), Barg, A. and Musin, O.R., Eds., Providence, RI: Amer. Math. Soc., 2014, pp. 93–109.

  2. Boltyanski, V.G., Martini, H., and Soltan, P.S., Excursions into Combinatorial Geometry, Berlin: Springer, 2012.

    MATH  Google Scholar 

  3. Berdnikov, A.V. and Raigorodskii, A.M., Bounds on Borsuk Numbers in Distance Graphs of a Special Type, Probl. Peredachi Inf., 2021, vol. 57, no. 2, pp. 44–50 [Probl. Inf. Transm. (Engl. Transl.), 2021, vol. 57, no. 2, pp. 136–142]. https://doi.org/10.1134/S0032946021020034

    MATH  Google Scholar 

  4. Agarwal, P.K. and Pach, J., Combinatorial Geometry, New York: Wiley, 2011.

    MATH  Google Scholar 

  5. Soifer, A., The Mathematical Coloring Book: Mathematics of Coloring and the Colorful Life of Its Creators, New York: Springer, 2009.

    Book  Google Scholar 

  6. Raigorodskii, A.M. and Koshelev, M.M., New Bounds on Clique-Chromatic Numbers of Johnson Graphs, Discrete Appl. Math., 2020, vol. 283, pp. 724–729. https://doi.org/10.1016/j.dam.2020.01.015

    Article  MathSciNet  Google Scholar 

  7. Ipatov, M.M., Koshelev, M.M., and Raigorodskii, A.M., Modularity of Some Distance Graphs, Dokl. Ross. Akad. Nauk, 2020, vol. 490, no. 1, pp. 71–73 [Dokl. Math. (Engl. Transl.), 2020, vol. 101, no. 1, pp. 60–61]. https://doi.org/10.1134/S1064562420010147

    MATH  Google Scholar 

  8. Bobu, A.V., Kupriyanov, A.É., and Raigorodskii, A.M., A Generalization of Kneser Graphs, Mat. Zametki, 2020, vol. 107, no. 3, pp. 351–365 [Math. Notes (Engl. Transl.), 2020, vol. 107, no. 3–4, pp. 392–403]. https://doi.org/10.1134/S0001434620030037

    Article  MathSciNet  Google Scholar 

  9. Bassalygo, L., Cohen, G., and Zémor, G., Codes with Forbidden Distances, Discrete Math., 2000, vol. 213, no. 1–3, pp. 3–11. https://doi.org/10.1016/S0012-365X(99)00161-2

    Article  MathSciNet  Google Scholar 

  10. MacWilliams, F.J. and Sloane, N.J.A., The Theory of Error-Correcting Codes, Amsterdam: North- Holland, 1977. Translated under the title Teoriya kodov, ispravlyayushchikh oshibki, Moscow: Svyaz’, 1979.

    MATH  Google Scholar 

  11. Graham, R.L., Rothschild, B.L., and Spencer, J.H., Ramsey Theory, New York: Wiley, 1990, 2nd ed.

    MATH  Google Scholar 

  12. Kupavskii, A. and Sagdeev, A., All Finite Sets Are Ramsey in the Maximum Norm, Forum Math. Sigma, 2021, vol. 9, Paper No. e55 (12 pp.). https://doi.org/10.1017/fms.2021.50

    Article  MathSciNet  Google Scholar 

  13. Nagy, Zs., A Ramsey-szám egy konstruktiv becslése (A Constructive Estimation of the Ramsey Number), Matem. Lapok, 1972, vol. 23, no. 3–4, pp. 301–302.

    Google Scholar 

  14. Mikhailov, K.A. and Raigorodskii, A.M., On the Ramsey Numbers for Complete Distance Graphs with Vertices in {0,1}n, Mat. Sb., 2009, vol. 200, no. 12, pp. 63–80 [Sb. Math. (Engl. Transl.), 2009, vol. 200, no. 12, pp. 1786–1806]. https://doi.org/10.1070/SM2009v200n12ABEH004059

    Article  MathSciNet  Google Scholar 

  15. Pushnyakov, Ph.A., A New Estimate for the Number of Edges in Induced Subgraphs of a Special Distance Graph, Probl. Peredachi Inf., 2015, vol. 51, no. 4, pp. 71–77 [Probl. Inf. Transm. (Engl. Transl.), 2015, vol. 51, no. 4, pp. 371–377]. https://doi.org/10.1134/S0032946015040067

    MathSciNet  MATH  Google Scholar 

  16. Pushnyakov, F.A., The Number of Edges in Induced Subgraphs of Some Distance Graphs, Mat. Zametki, 2019, vol. 105, no. 4, pp. 592–602 [Math. Notes (Engl. Transl.), 2019, vol. 105, no. 3–4, pp. 582–591]. https://doi.org/10.1134/S0001434619030313

    Article  MathSciNet  Google Scholar 

  17. Pushnyakov, F.A. and Raigorodskii, A.M., Estimate of the Number of Edges in Subgraphs of a Johnson Graph, Dokl. Ross. Akad. Nauk, 2021, vol. 499, no. 1, pp. 40–43 [Dokl. Math. (Engl. Transl.), 2021, vol. 104, no. 1, pp. 193–195]. https://doi.org/10.1134/S106456242104013X

    MATH  Google Scholar 

  18. Frankl, P. and Füredi, Z., Forbidding Just One Intersection, J. Combin. Theory Ser. A, 1985, vol. 39, no. 2, pp. 160–176. https://doi.org/10.1016/0097-3165(85)90035-4

    Article  MathSciNet  Google Scholar 

  19. Shabanov, L.E. and Raigorodskii, A.M., Turán Type Results for Distance Graphs, Discrete Comput. Geom., 2016, vol. 56, no. 3, pp. 814–832. https://doi.org/10.1007/s00454-016-9817-z

    Article  MathSciNet  Google Scholar 

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Acknowledgment

The author is deeply grateful to A.M. Raigorodskii for his comprehensive support, without which the paper would never appear. The author also expresses his gratitude to Maria Smetanina, a student of the Higher School of Economics, the artist of the drawings and diagrams.

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Translated from Problemy Peredachi Informatsii, 2021, Vol. 57, No. 4, pp. 79–86 https://doi.org/10.31857/S0555292321040070.

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Dubinin, N. New Turán Type Bounds for Johnson Graphs. Probl Inf Transm 57, 373–379 (2021). https://doi.org/10.1134/S0032946021040074

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  • DOI: https://doi.org/10.1134/S0032946021040074

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