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Hypergraphs with No Cycle of a Given Length
Published online by Cambridge University Press: 02 February 2012
Abstract
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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.
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- Combinatorics, Probability and Computing , Volume 21 , Issue 1-2: Honouring the Memory of Richard H. Schelp , March 2012 , pp. 193 - 201
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- Copyright © Cambridge University Press 2012
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