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New Bounds on the Modularity of Johnson Graphs and Random Subgraphs of Johnson Graphs

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Extended Abstracts EuroComb 2021

Part of the book series: Trends in Mathematics ((RPCRMB,volume 14))

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Abstract

In this paper we study the modularity of the so called Johnson graphs, also known as G(n, r, s) graphs. We obtain significant improvements for this value in case s and \(r \ge cs^2\) are fixed and n tends to infinity. We also obtain results on the modularity of random subgraphs of G(n, r, s) in Erdős–Rényi model.

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Acknowledgments

The work is done under the financial support of the grant of the president of the Russian Federation no. NSh-2540.2020.1. The second author is also supported by the grant of Theoretical Physics and Mathematics Advancement Foundation “BASIS”.

Author information

Authors and Affiliations

  1. Moscow Institute of Physics and Technology, Dolgoprudny, Russia

    Nikita Derevyanko

  2. Mechanics and Mathematics Faculty, Moscow State University, Moscow, Russia

    Mikhail Koshelev

  3. Laboratory of Advanced Combinatorics and Network Applications, Moscow Institute of Physics and Technology (State University), Dolgoprudny, Russia

    Andrei Raigorodskii

  4. Mechanics and Mathematics Faculty, Moscow State University, Moscow, Russia

    Andrei Raigorodskii

  5. Institute of Mathematics and Computer Science, Buryat State University, Ulan-Ude, Russia

    Andrei Raigorodskii

  6. Caucasus Mathematical Centre, Adyghe State University, Maykop, Russia

    Andrei Raigorodskii

Authors
  1. Nikita Derevyanko
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  2. Mikhail Koshelev
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  3. Andrei Raigorodskii
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Editor information

Editors and Affiliations

  1. Computer Science Institute, Charles University, Praha, Czech Republic

    Jaroslav Nešetřil

  2. Departament de Matemàtiques, Universitat Politècnica de Catalunya, Barcelona, Spain

    Guillem Perarnau

  3. Departament de Matemàtiques, Universitat Politècnica de Catalunya, Castelldefels, Spain

    Juanjo Rué

  4. Departament de Matemàtiques, Universitat Politècnica de Catalunya, Barcelona, Spain

    Oriol Serra

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Derevyanko, N., Koshelev, M., Raigorodskii, A. (2021). New Bounds on the Modularity of Johnson Graphs and Random Subgraphs of Johnson Graphs. In: Nešetřil, J., Perarnau, G., Rué, J., Serra, O. (eds) Extended Abstracts EuroComb 2021. Trends in Mathematics(), vol 14. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-83823-2_35

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