Skip to main content
    • Aa
    • Aa

Hypergraphs with No Cycle of a Given Length


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? *


Full text views

Total number of HTML views: 0
Total number of PDF views: 19 *
Loading metrics...

Abstract views

Total abstract views: 184 *
Loading metrics...

* Views captured on Cambridge Core between September 2016 - 21st September 2017. This data will be updated every 24 hours.