On regular hypergraphs of high girth

David Ellis, Nathan Linial

Research output: Contribution to journalArticlepeer-review

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

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics
  • Applied Mathematics

Fingerprint

Dive into the research topics of 'On regular hypergraphs of high girth'. Together they form a unique fingerprint.

Cite this