IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v163y2014i1d10.1007_s10957-013-0519-x.html
   My bibliography  Save this article

On the Largest Graph-Lagrangian of 3-Graphs with Fixed Number of Edges

Author

Listed:
  • Yanping Sun

    (Hunan University)

  • Qingsong Tang

    (Northeastern University
    Institute of Jilin University)

  • Cheng Zhao

    (Indiana State University
    Jilin University)

  • Yuejian Peng

    (Hunan University)

Abstract

The Graph-Lagrangian of a hypergraph has been a useful tool in hypergraph extremal problems. In most applications, we need an upper bound for the Graph-Lagrangian of a hypergraph. Frankl and Füredi conjectured that the $${r}$$ r -graph with $$m$$ m edges formed by taking the first $$\textit{m}$$ m sets in the colex ordering of the collection of all subsets of $${\mathbb N}$$ N of size $${r}$$ r has the largest Graph-Lagrangian of all $$r$$ r -graphs with $$m$$ m edges. In this paper, we show that the largest Graph-Lagrangian of a class of left-compressed $$3$$ 3 -graphs with $$m$$ m edges is at most the Graph-Lagrangian of the $$\mathrm 3 $$ 3 -graph with $$m$$ m edges formed by taking the first $$m$$ m sets in the colex ordering of the collection of all subsets of $${\mathbb N}$$ N of size $${3}$$ 3 .

Suggested Citation

  • Yanping Sun & Qingsong Tang & Cheng Zhao & Yuejian Peng, 2014. "On the Largest Graph-Lagrangian of 3-Graphs with Fixed Number of Edges," Journal of Optimization Theory and Applications, Springer, vol. 163(1), pages 57-79, October.
  • Handle: RePEc:spr:joptap:v:163:y:2014:i:1:d:10.1007_s10957-013-0519-x
    DOI: 10.1007/s10957-013-0519-x
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-013-0519-x
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.

    File URL: https://libkey.io/10.1007/s10957-013-0519-x?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Luana E. Gibbons & Donald W. Hearn & Panos M. Pardalos & Motakuri V. Ramana, 1997. "Continuous Characterizations of the Maximum Clique Problem," Mathematics of Operations Research, INFORMS, vol. 22(3), pages 754-768, August.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Biao Wu & Yuejian Peng, 2018. "Two extremal problems related to orders," Journal of Combinatorial Optimization, Springer, vol. 35(2), pages 588-612, February.
    2. Jingya Chang & Bin Xiao & Xin Zhang, 2023. "A Tensor Optimization Algorithm for Computing Lagrangians of Hypergraphs," Journal of Optimization Theory and Applications, Springer, vol. 198(2), pages 588-604, August.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Yuejian Peng & Qingsong Tang & Cheng Zhao, 2015. "On Lagrangians of r-uniform hypergraphs," Journal of Combinatorial Optimization, Springer, vol. 30(3), pages 812-825, October.
    2. Yanming Chang & Yuejian Peng & Yuping Yao, 2016. "Connection between a class of polynomial optimization problems and maximum cliques of non-uniform hypergraphs," Journal of Combinatorial Optimization, Springer, vol. 31(2), pages 881-892, February.
    3. Qingsong Tang & Xiangde Zhang & Guoren Wang & Cheng Zhao, 2018. "A continuous characterization of the maximum vertex-weighted clique in hypergraphs," Journal of Combinatorial Optimization, Springer, vol. 35(4), pages 1250-1260, May.
    4. Qingsong Tang & Xiangde Zhang & Cheng Zhao & Peng Zhao, 2022. "On the maxima of motzkin-straus programs and cliques of graphs," Journal of Global Optimization, Springer, vol. 84(4), pages 989-1003, December.
    5. Kovalyov, Mikhail Y. & Ng, C.T. & Cheng, T.C. Edwin, 2007. "Fixed interval scheduling: Models, applications, computational complexity and algorithms," European Journal of Operational Research, Elsevier, vol. 178(2), pages 331-342, April.
    6. Dellepiane, Umberto & Palagi, Laura, 2015. "Using SVM to combine global heuristics for the Standard Quadratic Problem," European Journal of Operational Research, Elsevier, vol. 241(3), pages 596-605.
    7. James T. Hungerford & Francesco Rinaldi, 2019. "A General Regularized Continuous Formulation for the Maximum Clique Problem," Management Science, INFORMS, vol. 44(4), pages 1161-1173, November.
    8. Stanislav Busygin & Sergiy Butenko & Panos M. Pardalos, 2002. "A Heuristic for the Maximum Independent Set Problem Based on Optimization of a Quadratic Over a Sphere," Journal of Combinatorial Optimization, Springer, vol. 6(3), pages 287-297, September.
    9. Ran Gu & Xueliang Li & Yuejian Peng & Yongtang Shi, 2016. "Some Motzkin–Straus type results for non-uniform hypergraphs," Journal of Combinatorial Optimization, Springer, vol. 31(1), pages 223-238, January.
    10. Hager, William W. & Hungerford, James T., 2015. "Continuous quadratic programming formulations of optimization problems on graphs," European Journal of Operational Research, Elsevier, vol. 240(2), pages 328-337.
    11. Qingsong Tang & Yuejian Peng & Xiangde Zhang & Cheng Zhao, 2014. "On Graph-Lagrangians of Hypergraphs Containing Dense Subgraphs," Journal of Optimization Theory and Applications, Springer, vol. 163(1), pages 31-56, October.
    12. Qingsong Tang & Yuejian Peng & Xiangde Zhang & Cheng Zhao, 2017. "On Motzkin–Straus type results for non-uniform hypergraphs," Journal of Combinatorial Optimization, Springer, vol. 34(2), pages 504-521, August.
    13. Immanuel M. Bomze & Michael Kahr & Markus Leitner, 2021. "Trust Your Data or Not—StQP Remains StQP: Community Detection via Robust Standard Quadratic Optimization," Mathematics of Operations Research, INFORMS, vol. 46(1), pages 301-316, February.
    14. Vargas, Luis Felipe & Laurent, Monique, 2023. "Copositive matrices, sums of squares and the stability number of a graph," Other publications TiSEM 8e471691-a452-4ee5-9f88-8, Tilburg University, School of Economics and Management.
    15. Zehui Jia & Xue Gao & Xingju Cai & Deren Han, 2021. "Local Linear Convergence of the Alternating Direction Method of Multipliers for Nonconvex Separable Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 188(1), pages 1-25, January.
    16. Jacek Gondzio & E. Alper Yıldırım, 2021. "Global solutions of nonconvex standard quadratic programs via mixed integer linear programming reformulations," Journal of Global Optimization, Springer, vol. 81(2), pages 293-321, October.
    17. Nicolas Gillis & François Glineur, 2014. "A continuous characterization of the maximum-edge biclique problem," Journal of Global Optimization, Springer, vol. 58(3), pages 439-464, March.
    18. Riccardo Bisori & Matteo Lapucci & Marco Sciandrone, 2022. "A study on sequential minimal optimization methods for standard quadratic problems," 4OR, Springer, vol. 20(4), pages 685-712, December.
    19. Seyedmohammadhossein Hosseinian & Dalila B. M. M. Fontes & Sergiy Butenko, 2018. "A nonconvex quadratic optimization approach to the maximum edge weight clique problem," Journal of Global Optimization, Springer, vol. 72(2), pages 219-240, October.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:joptap:v:163:y:2014:i:1:d:10.1007_s10957-013-0519-x. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.