On regular hypergraphs of high girth

David Ellis, Nathan Linial

Research output: Contribution to journalArticlepeer-review

13 Scopus citations

Abstract

We give lower bounds on the maximum possible girth of an r-uniform, d-regular hypergraph with at most n vertices, using the definition of a hypergraph cycle due to Berge. These differ from the trivial upper bound by an absolute constant factor (viz., by a factor of between 3/2+o(1) and 2+o(1)). We also define a random r-uniform 'Cayley' hypergraph on the symmetric group Sn which has girth Ω(√ log |Sn|) with high probability, in contrast to random regular r-uniform hypergraphs, which have constant girth with positive probability.

Original languageAmerican English
JournalElectronic Journal of Combinatorics
Volume21
Issue number1
DOIs
StatePublished - 10 Mar 2014

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