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# Optimal Divisibility Conditions for Loose Hamilton Cycles in Random Hypergraphs

@article{Dudek2012OptimalDC, title={Optimal Divisibility Conditions for Loose Hamilton Cycles in Random Hypergraphs}, author={Andrzej Dudek and Alan M. Frieze and Po-Shen Loh and Shelley Speiss}, journal={Electr. J. Comb.}, year={2012}, volume={19}, pages={P44} }

- Published 2012 in Electr. J. Comb.

In the random k-uniform hypergraph H (k) n,p of order n, each possible k-tuple appears independently with probability p. A loose Hamilton cycle is a cycle of order n in which every pair of consecutive edges intersects in a single vertex. It was shown by Frieze that if p ≥ c(log n)/n2 for some absolute constant c > 0, then a.a.s. H (3) n,p contains a loose Hamilton cycle, provided that n is divisible by 4. Subsequently, Dudek and Frieze extended this result for any uniformity k ≥ 4, proving that… CONTINUE READING