منابع مشابه
Packing Hamilton Cycles Online
It is known that w.h.p. the hitting time τ2σ for the random graph process to have minimum degree 2σ coincides with the hitting time for σ edge disjoint Hamilton cycles, [4], [13], [9]. In this paper we prove an online version of this property. We show that, for a fixed integer σ ≥ 2, if random edges of Kn are presented one by one then w.h.p. it is possible to color the edges online with σ color...
متن کاملLoose 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 کاملPacking Tight Hamilton Cycles in Uniform Hypergraphs
We say that a k-uniform hypergraph C is a Hamilton cycle of type `, for some 1 ≤ ` ≤ k, if there exists a cyclic ordering of the vertices of C such that every edge consists of k consecutive vertices and for every pair of consecutive edges Ei−1, Ei in C (in the natural ordering of the edges) we have |Ei−1 \ Ei| = `. We define a class of ( , p)-regular hypergraphs, that includes random hypergraph...
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ژورنال
عنوان ژورنال: Combinatorics, Probability and Computing
سال: 2017
ISSN: 0963-5483,1469-2163
DOI: 10.1017/s0963548317000402