On Regular Hypergraphs of High Girth
Electronic Journal of Combinatorics
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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(sqroot(log |S_n|)) with high probability, in contrast to random regular r-uniform hypergraphs, which have constant girth with positive probability.
AuthorsELLIS, DC; Linial, N