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 - <p style="text-align: justify;">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.</p>