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Loose Hamilton Cycles in Random 3Uniform Hypergraphs
, 2010
"... 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,...,y n/2 are all distinct. We prove that there exists an absolute constant K> ..."
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Cited by 6 (6 self)
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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,...,y n/2 are all distinct. We prove that there exists an absolute constant K> 0 such that if p � K log n n 2 then lim n→∞ 4n Pr(Hn,p;3 contains a loose Hamilton cycle) = 1.
Loose Hamilton Cycles in Random kUniform Hypergraphs
, 2010
"... In the random hypergraph Hn,p;k each possible ktuple appears independently with probability p. A loose Hamilton cycle is a cycle in which every pair of adjacent edges intersects in a single vertex. We prove that if pn k−1 / log n tends to infinity with n then lim Pr(Hn,p;k contains a loose Hamilton ..."
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Cited by 2 (2 self)
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In the random hypergraph Hn,p;k each possible ktuple appears independently with probability p. A loose Hamilton cycle is a cycle in which every pair of adjacent edges intersects in a single vertex. We prove that if pn k−1 / log n tends to infinity with n then lim Pr(Hn,p;k contains a loose Hamilton cycle) = 1. n→∞ 2(k−1)n 1
On Generalized Random Railways
 Combin. Probab. Comput
"... We consider a random generalized railway defined as a random 3regular multigraph where some vertices are regarded as switches not allowing tra#c between any pair of attached edges. It is shown that the probability that the generalized railway is functioning is linear in the proportion of switch ..."
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Cited by 1 (1 self)
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We consider a random generalized railway defined as a random 3regular multigraph where some vertices are regarded as switches not allowing tra#c between any pair of attached edges. It is shown that the probability that the generalized railway is functioning is linear in the proportion of switches. Thus there is no threshold phenomenon for this property.
Multicoloured Hamilton cycles in random edgecoloured graphs
, 2002
"... We define a space of random edgecoloured graphs n,m,n which correspond naturally to edge ncolourings of Gn,m. We show that there exist constants K0, K1 _ 21 such that provided m _ Kon log n and n _ Kin then a random edge coloured graph contains a multicoloured Hamilton cycle with probability ..."
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Cited by 1 (1 self)
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We define a space of random edgecoloured graphs n,m,n which correspond naturally to edge ncolourings of Gn,m. We show that there exist constants K0, K1 _ 21 such that provided m _ Kon log n and n _ Kin then a random edge coloured graph contains a multicoloured Hamilton cycle with probability tending to 1, as the number of vertices n tends to infinity.
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"... Optimal divisibility conditions for loose Hamilton cycles in random hypergraphs ..."
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Optimal divisibility conditions for loose Hamilton cycles in random hypergraphs