Loose Hamilton Cycles in Random 3-Uniform Hypergraphs
نویسنده
چکیده
In the random hypergraph H = Hn,p;3 each possible triple appears independently with probability p. A loose Hamilton cycle can be described as a sequence of edges {xi, yi, xi+1} for i = 1, 2, . . . , n/2 where x1, x2, . . . , xn/2, y1, y2, . . . , yn/2 are all distinct. We prove that there exists an absolute constant K > 0 such that if p > K logn n then lim n→∞ 4|n Pr(Hn,p;3 contains a loose Hamilton cycle) = 1.
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ورودعنوان ژورنال:
- Electr. J. Comb.
دوره 17 شماره
صفحات -
تاریخ انتشار 2010