منابع مشابه
Loose Hamilton cycles in hypergraphs
We prove that any k-uniform hypergraph on n vertices with minimum degree at least n 2(k−1) + o(n) contains a loose Hamilton cycle. The proof strategy is similar to that used by Kühn and Osthus for the 3-uniform case. Though some additional difficulties arise in the k-uniform case, our argument here is considerably simplified by applying the recent hypergraph blow-up lemma of Keevash.
متن کاملLoose Hamilton Cycles in Regular Hypergraphs
We establish a relation between two uniform models of random k-graphs (for constant k ≥ 3) on n labeled vertices: H(k)(n,m), the random k-graph with exactly m edges, and H(k)(n, d), the random d-regular k-graph. By extending to k-graphs the switching technique of McKay and Wormald, we show that, for some range of d = d(n) and a constant c > 0, if m ∼ cnd, then one can couple H(k)(n,m) and H(k)(...
متن کاملLoose 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.
متن کاملDirac-type results for loose Hamilton cycles in uniform hypergraphs
A classic result of G. A. Dirac in graph theory asserts that every n-vertex graph (n ≥ 3) with minimum degree at least n/2 contains a spanning (so-called Hamilton) cycle. G. Y. Katona and H. A. Kierstead suggested a possible extension of this result for k-uniform hypergraphs. There a Hamilton cycle of an n-vertex hypergraph corresponds to an ordering of the vertices such that every k consecutiv...
متن کاملLoose Hamilton Cycles in Random 3-Uniform Hypergraphs
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: Discrete Mathematics
سال: 2011
ISSN: 0012-365X
DOI: 10.1016/j.disc.2010.11.013