We show that for every rational number r∈(1,2)of the form 2-a/b,where a,b∈N^(+)satisfy[b/a]^(3)≤a≤b/([b/a]+1)+1,there exists a graph Frsuch that the Turán number ex(n,F_(r))=Θ(n^(r)).Our result in particular...We show that for every rational number r∈(1,2)of the form 2-a/b,where a,b∈N^(+)satisfy[b/a]^(3)≤a≤b/([b/a]+1)+1,there exists a graph Frsuch that the Turán number 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.展开更多
基金supported in part by U.S.taxpayers through the National Science Foundation(NSF)grant DMS-1855542by U.S.taxpayers through NSF grant DMS-1953946+3 种基金supported in part by an AMS Simons Travel Grantsupported in part by the National Key R&D Program of China 2020YFA0713100National Natural Science Foundation of China grants 11622110 and 12125106Anhui Initiative in Quantum Information Technologies grant AHY150200。
文摘We show that for every rational number r∈(1,2)of the form 2-a/b,where a,b∈N^(+)satisfy[b/a]^(3)≤a≤b/([b/a]+1)+1,there exists a graph Frsuch that the Turán number 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.
