Higher Dimensional Moore Bounds

Goff, Michael

doi:10.1007/s00373-010-0979-9

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“…In this paper, we considered a very simple and purely combinatorial notion of girth in hypergraphs, but other notions appear in the literature, for example using the language of simplicial topology, such as in [24,14]. A different combinatorial definition was introduced by Erdős in [11].…”

Section: Conclusion and Open Problemsmentioning

confidence: 99%

On Regular Hypergraphs of High Girth

Ellis

Linial

2014

Electron. J. Combin.

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We give lower bounds on the maximum possible girth of an runiform, 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 S n which has girth Ω(n 1/3 ) with high probability, in contrast to random regular r-uniform hypergraphs, which have constant girth with positive probability.

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Section: Conclusion and Open Problemsmentioning

confidence: 99%