Skip to main content
    • Aa
    • Aa
  • Get access
    Check if you have access via personal or institutional login
  • Cited by 1
  • Cited by
    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Kostochka, Alexandr Mubayi, Dhruv and Verstraëte, Jacques 2015. Turán problems and shadows I: Paths and cycles. Journal of Combinatorial Theory, Series A, Vol. 129, p. 57.


Hypergraphs with No Cycle of a Given Length

  • DOI:
  • Published online: 02 February 2012

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.

Linked references
Hide All

This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

[1]B. Bollobás and E. Győri (2008) Pentagons vs. triangles. Discrete Math. 308 43324336.

[2]J. A. Bondy and M. Simonovits (1974) Cycles of even length in graphs. J. Combin. Theory Ser. B 16 97105.

[3]P. Erdős and T. Gallai (1959) On maximal paths and circuits of graphs. Acta Math. Acad. Sci. Hungar. 10 337356.

[4]A. Gyárfás , M. Jacobson , A. Kézdy and J. Lehel (2006) Odd cycles and Theta-cycles in hypergraphs. Discrete Math. 306 24812491.

[7]A. Kostochka and J. Verstraete (2005) Even cycles in hypergraphs. J. Combin. Theory Ser. B 94 173182.

Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Combinatorics, Probability and Computing
  • ISSN: 0963-5483
  • EISSN: 1469-2163
  • URL: /core/journals/combinatorics-probability-and-computing
Please enter your name
Please enter a valid email address
Who would you like to send this to? *