کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4949680 | 1440198 | 2017 | 8 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
The connection between polynomial optimization, maximum cliques and Turán densities
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
مهندسی کامپیوتر
نظریه محاسباتی و ریاضیات
پیش نمایش صفحه اول مقاله
![عکس صفحه اول مقاله: The connection between polynomial optimization, maximum cliques and Turán densities The connection between polynomial optimization, maximum cliques and Turán densities](/preview/png/4949680.png)
چکیده انگلیسی
In 1965, Motzkin-Straus established the connection between the maximum cliques and the Lagrangian of a graph, the maximum value of a quadratic function determined by a graph in the standard simplex. This connection gave a proof of the Turán's classical result on Turán densities of complete graphs. In 1980's, Sidorenko and Frankl-Füredi further developed this method for hypergraph Turán problems. However, the connection between the Lagrangian and the maximum cliques of a graph cannot be extended to hypergraphs. In 2009, S. Rota Bulò and M. Pelillo defined a homogeneous polynomial function of degree r determined by an r-uniform hypergraph and gave the connection between the minimum value of this polynomial function and the maximum cliques of an r-uniform hypergraph. In this paper, we provide a connection between the local (global) minimizers of non-homogeneous polynomial functions to the maximal (maximum) cliques of hypergraphs whose edges containing râ1 and r vertices. This connection can be applied to obtain an upper bound on the Turán densities of complete {râ1,r}-type hypergraphs.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Discrete Applied Mathematics - Volume 225, 10 July 2017, Pages 114-121
Journal: Discrete Applied Mathematics - Volume 225, 10 July 2017, Pages 114-121
نویسندگان
Biao Wu, Yuejian Peng,