Recently, the authors gave upper bounds for the size of 3-uniform hypergraphs avoiding a given odd cycle using the definition of a cycle due to Berge. In the present paper we extend this bound to m-uniform hypergraphs (for all m ≥ 3), as well as m-uniform hypergraphs avoiding a cycle of length 2k. Finally we consider non-uniform hypergraphs avoiding cycles of length 2k or 2k + 1. In both cases we can bound |h| by O(n1+1/k) under the assumption that all h ∈ ε() satisfy |h| ≥ 4k2.
(Received March 31 2011)
(Revised November 10 2011)
(Online publication February 02 2012)
† Research partially supported by the Hungarian OTKA Grant NK 78439 and by ToK project FIST of the Rényi Institute in the sixth framework programme of the European Union.
‡ Research partially supported by ToK project FIST of Rényi Institute in the sixth framework programme of the European Union.