On hypergraphs without loose cycles

摘要

Recently, Mubayi and Wang showed that for r = 4 and l = 3, the number of n-vertex r-graphs that do not contain any loose cycle of length l is at most 2(0(nr-1(log) (n)(r-3)/(r-2))). We improve this bound to 2(0(nr-1 log log) (n)). (C) 2017 Elsevier B.V. All rights reserved.