Year: 2022
Author: Tao Jiang, Zilin Jiang, Jie Ma
Annals of Applied Mathematics, Vol. 38 (2022), Iss. 3 : pp. 356–384
Abstract
We show that for every rational number $r∈(1,2)$ of the form $2−a/b,$ where $a, b∈\mathbb{N}^+$ satisfy $$\lfloor b/a\rfloor ^3 ≤a≤b/(\lfloor b/a\rfloor +1)+1,$$ there exists a graph $F_r$ such that the Turán number ${\rm ex}(n,F_r)=Θ(n^r).$ Our result in particular generates infinitely many new Turán exponents. As a byproduct, we formulate a framework that is taking shape in recent work on the Bukh–Conlon conjecture.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aam.OA-2022-0008
Annals of Applied Mathematics, Vol. 38 (2022), Iss. 3 : pp. 356–384
Published online: 2022-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 29
Keywords: Extremal graph theory turán exponents bipartite graphs.
Author Details
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Turán Number of Nonbipartite Graphs and the Product Conjecture
Peng, Xing
Song, Ge
Yuan, Long-Tu
(2023)
https://doi.org/10.1007/s40304-023-00375-1 [Citations: 0]