Abstract
We present results from two papers by the authors on analysis of d-regular k-uniform hypergraphs, when k is fixed and the number n of vertices tends to infinity. The first result is approximate enumeration of such hypergraphs, provided d = d(n) = o(n k), where k = k (k) = 1 for all k ≥ 4, while k(3) = 1/2. The second result is that a random d-regular hypergraph contains as a dense sub-graph the uniform random hypergraph (a generalization of the Erdős-Rényi uniform graph), and, in view of known results, contains a loose Hamilton cycle with probability tending to one.
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Dudek, A., Frieze, A., Ruciński, A., Šileikis, M. (2013). Regular hypergraphs: asymptotic counting and loose Hamilton cycles. In: Nešetřil, J., Pellegrini, M. (eds) The Seventh European Conference on Combinatorics, Graph Theory and Applications. CRM Series, vol 16. Edizioni della Normale, Pisa. https://doi.org/10.1007/978-88-7642-475-5_77
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DOI: https://doi.org/10.1007/978-88-7642-475-5_77
Publisher Name: Edizioni della Normale, Pisa
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