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On Turán numbers of the complete 4-graphs
Discrete Mathematics ( IF 0.7 ) Pub Date : 2021-07-14 , DOI: 10.1016/j.disc.2021.112544
Alexander Sidorenko 1
Affiliation  

The Turán number T(n,α+1,r) is the minimum number of edges in an n-vertex r-graph whose independence number does not exceed α. For each r2, there exists t(r) such that T(n,α+1,r)=t(r)nrα1r(1+o(1)) as α/r and n/α. It is known that t(2)=1/2, and the conjectured value of t(3) is 2/3. We prove that t(4)<0.706335.



中文翻译:

关于完全四图的图兰数

图兰数 (n,α+1,r)是独立数不超过αn顶点r图中的最小边数。对于每个r2, 那里存在 (r) 以至于 (n,α+1,r)=(r)nrα1-r(1+(1)) 作为 α/rn/α. 众所周知(2)=1/2, 的推测值 (3)是 2/3。我们证明(4)<0.706335.

更新日期:2021-07-15
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