Powers of Hamilton cycles in random graphs and tight Hamilton cycles in random hypergraphs
نویسندگان
چکیده
منابع مشابه
Tight Hamilton cycles in random hypergraphs
We give an algorithmic proof for the existence of tight Hamilton cycles in a random r-uniform hypergraph with edge probability p = n−1+ε for every ε > 0. This partly answers a question of Dudek and Frieze [Random Structures Algorithms], who used a second moment method to show that tight Hamilton cycles exist even for p = ω(n)/n (r ≥ 3) where ω(n) → ∞ arbitrary slowly, and for p = (e + o(1))/n (...
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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.
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ژورنال
عنوان ژورنال: Random Structures & Algorithms
سال: 2018
ISSN: 1042-9832
DOI: 10.1002/rsa.20782