Volume 38, Issue 3
Negligible Obstructions and Turán Exponents

Tao Jiang, Zilin Jiang & Jie Ma

Ann. Appl. Math., 38 (2022), pp. 356-384.

Published online: 2022-08

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  • 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.

  • AMS Subject Headings

05C35

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COPYRIGHT: © Global Science Press

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@Article{AAM-38-356, author = {Jiang , TaoJiang , Zilin and Ma , Jie}, title = {Negligible Obstructions and Turán Exponents}, journal = {Annals of Applied Mathematics}, year = {2022}, volume = {38}, number = {3}, pages = {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.

}, issn = {}, doi = {https://doi.org/10.4208/aam.OA-2022-0008}, url = {http://global-sci.org/intro/article_detail/aam/20881.html} }
TY - JOUR T1 - Negligible Obstructions and Turán Exponents AU - Jiang , Tao AU - Jiang , Zilin AU - Ma , Jie JO - Annals of Applied Mathematics VL - 3 SP - 356 EP - 384 PY - 2022 DA - 2022/08 SN - 38 DO - http://doi.org/10.4208/aam.OA-2022-0008 UR - https://global-sci.org/intro/article_detail/aam/20881.html KW - Extremal graph theory, turán exponents, bipartite graphs. AB -

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.

Tao Jiang, Zilin Jiang & Jie Ma. (2022). Negligible Obstructions and Turán Exponents. Annals of Applied Mathematics. 38 (3). 356-384. doi:10.4208/aam.OA-2022-0008
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