A decomposition of complete bipartite 4-uniform hypergraphs K_4^{5,5} into loose cycles of length 5,10
نویسندگان
چکیده
منابع مشابه
Loose Hamilton Cycles in Random Uniform Hypergraphs
In the random k-uniform hypergraph Hn,p;k 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 adjacent edges intersects in a single vertex. We prove that if pnk−1/ log n tends to infinity with n then lim n→∞ 2(k−1)|n Pr(Hn,p;k contains a loose Hamilton cycle) = 1. This is asymptotically best possible.
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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 Ham...
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ژورنال
عنوان ژورنال: International Mathematical Forum
سال: 2013
ISSN: 1314-7536
DOI: 10.12988/imf.2013.39179