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

Danyal Soybas; Onur Alp Ilhan

doi:doi:10.11648/j.ml.20150103.11

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

Danyal Soybas, Onur Alp Ilhan

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

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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.

DOI	10.11648/j.ml.20150103.11
Published in	Mathematics Letters (Volume 1, Issue 3, October 2015)
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), 2024. 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.

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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

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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

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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

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@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}
}

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T1  - A Partial Answer to Sidorenko’s Conjecture on a Correlation Inequality for Bipartite Graphs
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AU  - Onur Alp Ilhan
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VL  - 1
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Author Information

Danyal Soybas

Department of Mathematics, Faculty of Education, Erciyes University, Kayseri, Turkey
Onur Alp Ilhan

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

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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

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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

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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