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| Negligible Obstructions and Tur´anExponents |
| Tao Jiang,Zilin Jiang,Jie Ma |
| (Department of Mathematics, Miami Univeristy, Oxford, OH 45056, USA;School of Mathematical and Statistical Sciences, and School of Computing
and Augmented Intelligence, Arizona State University, Tempe, AZ 85281,USA;School of Mathematical Sciences, University of Science and Technology
of China, Hefei, Anhui 230026, China) |
| DOI： |
| Abstract: |
| We show that for every rational number r∈(1,2) of the form 2?a/b,
where a,b∈N
+ satisfy
b
b/ac 3 ≤a≤b/(b b/ac +1)+1,
there exists a graph Fr such that the Tur′an number ex(n,Fr)=Θ(n
r
). Our result
in particular generates infinitely many new Tur′an exponents. As a byproduct,
we formulate a framework that is taking shape in recent work on the Bukh–
Conlon conjecture. |
| Key words: Extremal graph theory, tur´an exponents, bipartite graphs. |