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Hypergraphs with No Cycle of a Given Length

Published online by Cambridge University Press:  02 February 2012

ERVIN GYŐRI  and
NATHAN LEMONS
ERVIN GYŐRI
Affiliation:
Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences, Budapest H-1364, PO box 127, Hungary (e-mail: ervin@renyi.hu, nathan@renyi.hu)
NATHAN LEMONS
Affiliation:
Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences, Budapest H-1364, PO box 127, Hungary (e-mail: ervin@renyi.hu, nathan@renyi.hu)
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Abstract

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.

Type
Paper
Information
Combinatorics, Probability and Computing , Volume 21 , Issue 1-2: Honouring the Memory of Richard H. Schelp , March 2012 , pp. 193 - 201
Copyright
Copyright © Cambridge University Press 2012

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