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167,259
On Perfect Matchings in Uniform Hypergraphs with . . .
, 2009
"... We study sufficient ℓdegree (1 ≤ ℓ < k) conditions for the appearance of perfect and nearly perfect matchings in kuniform hypergraphs. In particular, we obtain a minimum vertex degree condition (ℓ = 1) for 3uniform hypergraphs, which is approximately tight, by showing that every 3uniform hyp ..."
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Cited by 29 (4 self)
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We study sufficient ℓdegree (1 ≤ ℓ < k) conditions for the appearance of perfect and nearly perfect matchings in kuniform hypergraphs. In particular, we obtain a minimum vertex degree condition (ℓ = 1) for 3uniform hypergraphs, which is approximately tight, by showing that every 3uniform
Matchings in hypergraphs of large minimum degree
 J. Graph Theory
, 2006
"... It is well known that every bipartite graph with vertex classes of size n whose minimum degree is at least n/2 contains a perfect matching. We prove an analogue of this result for hypergraphs. We also prove several related results which guarantee the existence of almost perfect matchings in runifor ..."
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Cited by 26 (4 self)
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It is well known that every bipartite graph with vertex classes of size n whose minimum degree is at least n/2 contains a perfect matching. We prove an analogue of this result for hypergraphs. We also prove several related results which guarantee the existence of almost perfect matchings in runiform
A note on perfect matchings in uniform hypergraphs with large minimum collective degree
"... For an integer k ≥ 2 and a kuniform hypergraph H, let δk−1(H) be the largest integer d such that every (k − 1)element set of vertices of H belongs to at least d edges of H. Further, let t(k, n) be the smallest integer t such that every kuniform hypergraph on n vertices and with δk−1(H) ≥ t cont ..."
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Cited by 10 (3 self)
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) ≥ t contains a perfect matching. The parameter t(k, n) has been completely determined for all k and large n divisible by k by Rödl, Ruciński, and Szemerédi in [Perfect matchings in large uniform hypergraphs with large minimum collective degree, submitted]. The values of t(k, n) are very close to n/2−k. In fact
Perfect matchings in 4uniform hypergraphs
"... A perfect matching in a 4uniform hypergraph is a subset of bn4 c disjoint edges. We prove that if H is a sufficiently large 4uniform hypergraph on n = 4k vertices such that every vertex belongs to more than n−1 3) − (3n/43) edges then H contains a perfect matching. This bound is tight and settles ..."
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Cited by 6 (0 self)
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A perfect matching in a 4uniform hypergraph is a subset of bn4 c disjoint edges. We prove that if H is a sufficiently large 4uniform hypergraph on n = 4k vertices such that every vertex belongs to more than n−1 3) − (3n/43) edges then H contains a perfect matching. This bound is tight and settles
Perfect Matchings in Random Uniform Hypergraphs
 Random Structures Algorithms
, 2001
"... In the random kuniform hypergraph k (n, p) on a vertex set V of size n, each subset of size k of V independently belongs to it with probability p. Motivated by a theorem of Erdos and Renyi [6] regarding when a random graph G(n, p) = 2 (n, p) has a perfect matching, Schmidt and Shamir [14] essen ..."
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Cited by 10 (0 self)
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In the random kuniform hypergraph k (n, p) on a vertex set V of size n, each subset of size k of V independently belongs to it with probability p. Motivated by a theorem of Erdos and Renyi [6] regarding when a random graph G(n, p) = 2 (n, p) has a perfect matching, Schmidt and Shamir [14
Perfect matching in 3uniform hypergraphs with large vertex degree
"... A perfect matching in a 3uniform hypergraph on n = 3k vertices is a subset of n3 disjoint edges. We prove that if H is a 3uniform hypergraph on n = 3k vertices such that every vertex belongs to at least n−1 2) − (2n/32) + 1 edges then H contains a perfect matching. We give a construction to show ..."
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Cited by 15 (1 self)
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A perfect matching in a 3uniform hypergraph on n = 3k vertices is a subset of n3 disjoint edges. We prove that if H is a 3uniform hypergraph on n = 3k vertices such that every vertex belongs to at least n−1 2) − (2n/32) + 1 edges then H contains a perfect matching. We give a construction to show
Exact minimum degree thresholds for perfect matchings in uniform hypergraphs
 J. Combin. Theory A
"... ar ..."
SIMPLIcity: SemanticsSensitive Integrated Matching for Picture LIbraries
 IEEE Transactions on Pattern Analysis and Machine Intelligence
, 2001
"... The need for efficient contentbased image retrieval has increased tremendously in many application areas such as biomedicine, military, commerce, education, and Web image classification and searching. We present here SIMPLIcity (Semanticssensitive Integrated Matching for Picture LIbraries), an imag ..."
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Cited by 541 (35 self)
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The need for efficient contentbased image retrieval has increased tremendously in many application areas such as biomedicine, military, commerce, education, and Web image classification and searching. We present here SIMPLIcity (Semanticssensitive Integrated Matching for Picture LIbraries
A Critical Point For Random Graphs With A Given Degree Sequence
, 2000
"... Given a sequence of nonnegative real numbers 0 ; 1 ; : : : which sum to 1, we consider random graphs having approximately i n vertices of degree i. Essentially, we show that if P i(i \Gamma 2) i ? 0 then such graphs almost surely have a giant component, while if P i(i \Gamma 2) i ! 0 the ..."
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Cited by 511 (8 self)
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Given a sequence of nonnegative real numbers 0 ; 1 ; : : : which sum to 1, we consider random graphs having approximately i n vertices of degree i. Essentially, we show that if P i(i \Gamma 2) i ? 0 then such graphs almost surely have a giant component, while if P i(i \Gamma 2) i ! 0
Results 1  10
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167,259