| Peer-Reviewed

A Partial Answer to Sidorenko’s Conjecture on a Correlation Inequality for Bipartite Graphs

Received: 26 October 2015     Accepted: 23 December 2015     Published: 5 January 2016
Views:       Downloads:
Abstract

Sidorenko conjectured an integral inequality for a product of functions h(xi, yi) where the diagram of the product is a bipartite graph G in [8]. We answered the conjecture positively when the function h is multiplicative or additive separable with respect to variables x and y.

Published in Mathematics Letters (Volume 1, Issue 3)
DOI 10.11648/j.ml.20150103.11
Page(s) 17-19
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2016. Published by Science Publishing Group

Keywords

Sidorenko’s Conjecture, Bipartite Graph, Lebesgue Measure, Measurable Function

References
[1] Johnson P., Soybaş D., An Integral Inequality For Probability Spaces, International Journal of Mathematics and Computer Science, vol. 8, pp. 1-3, 2013.
[2] Sidorenko, A. F, Inequalities for functional generated by bipartite graphs (in Russian), Discrete Mathematics and Applications 3 (3) 50-65 (1991).
[3] Sidorenko, A. F., Exremal problems in graph theory and inequalities in functional analysis (in Russian). In Lupanov, O. B, ed., Proceedings of the Soviet Seminar on Discrete Mathematics and it Applications (in Russian), pp. 99-105. Moscow: Moscow State University 1986, MR88m: 05053.
[4] Mulholland, H. P., Smith, C. A. B., An inequality arising in genetical theory, Amer. Math. Mon. 66, 673-683 (1959).
[5] Blakley, G. R, Roy, P., Hölder type inequality for symmetrical matrices with nonnegative entries. Proc. Am. Math. Soc. 16, 1244-1245 (1965).
[6] Atkinson, F. V., Watterson, G. A., Moran, P. A. D., A matrix inequality. Q. J. Math. Oxf. II Ser. 11, 137-140 (1960).
[7] London, D., Two equalities in nonnegative symmetric matrices. Pac. J. Math.16, 515-536(1966).
[8] Sidorenko, A., A Correlation Inequality for Bipartite Graphs., Graphs and Combinatorics (1993) 9, 201-204.
Cite This Article
  • APA Style

    Danyal Soybas, Onur Alp Ilhan. (2016). A Partial Answer to Sidorenko’s Conjecture on a Correlation Inequality for Bipartite Graphs. Mathematics Letters, 1(3), 17-19. https://doi.org/10.11648/j.ml.20150103.11

    Copy | Download

    ACS Style

    Danyal Soybas; Onur Alp Ilhan. A Partial Answer to Sidorenko’s Conjecture on a Correlation Inequality for Bipartite Graphs. Math. Lett. 2016, 1(3), 17-19. doi: 10.11648/j.ml.20150103.11

    Copy | Download

    AMA Style

    Danyal Soybas, Onur Alp Ilhan. A Partial Answer to Sidorenko’s Conjecture on a Correlation Inequality for Bipartite Graphs. Math Lett. 2016;1(3):17-19. doi: 10.11648/j.ml.20150103.11

    Copy | Download

  • @article{10.11648/j.ml.20150103.11,
      author = {Danyal Soybas and Onur Alp Ilhan},
      title = {A Partial Answer to Sidorenko’s Conjecture on a Correlation Inequality for Bipartite Graphs},
      journal = {Mathematics Letters},
      volume = {1},
      number = {3},
      pages = {17-19},
      doi = {10.11648/j.ml.20150103.11},
      url = {https://doi.org/10.11648/j.ml.20150103.11},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ml.20150103.11},
      abstract = {Sidorenko conjectured an integral inequality for a product of functions h(xi, yi) where the diagram of the product is a bipartite graph G in [8]. We answered the conjecture positively when the function h is multiplicative or additive separable with respect to variables x and y.},
     year = {2016}
    }
    

    Copy | Download

  • TY  - JOUR
    T1  - A Partial Answer to Sidorenko’s Conjecture on a Correlation Inequality for Bipartite Graphs
    AU  - Danyal Soybas
    AU  - Onur Alp Ilhan
    Y1  - 2016/01/05
    PY  - 2016
    N1  - https://doi.org/10.11648/j.ml.20150103.11
    DO  - 10.11648/j.ml.20150103.11
    T2  - Mathematics Letters
    JF  - Mathematics Letters
    JO  - Mathematics Letters
    SP  - 17
    EP  - 19
    PB  - Science Publishing Group
    SN  - 2575-5056
    UR  - https://doi.org/10.11648/j.ml.20150103.11
    AB  - Sidorenko conjectured an integral inequality for a product of functions h(xi, yi) where the diagram of the product is a bipartite graph G in [8]. We answered the conjecture positively when the function h is multiplicative or additive separable with respect to variables x and y.
    VL  - 1
    IS  - 3
    ER  - 

    Copy | Download

Author Information
  • Department of Mathematics, Faculty of Education, Erciyes University, Kayseri, Turkey

  • Department of Mathematics, Faculty of Education, Erciyes University, Kayseri, Turkey

  • Sections