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Abstract: For every fixed k 3 there exists a constant c k with the following property. Let H be a k- uniform, D-regular hypergraph on N vertices, in which no two edges contain more than one common vertex. If k ? 3 then H contains a matching covering all vertices but at most c k ND \Gamma1=(k\Gamma1) : If k = 3, then H contains a matching covering all vertices but at most c 3 ND \Gamma1=2 ln 3=2 D. This improves previous estimates and implies, for example, that any Steiner Triple System on N... (Update)
Context of citations to this paper: More
.... of a new martingale inequality which the second author recently developed, improving on results of Kim [16] and Alon, Kim and Spencer [2]. The inequality provides a methodology for proving sharp concentration results for not necessarily dependent random variables which yields...
...G(n; p) is d regular is much higher than . The rst step relies on a sharp concentration inequality obtained by Alon, Kim and Spencer [1]. The latter follows directly from an estimate of Shamir and Upfal [12] 3 Erd os R enyi revisited In this section, we prove the following...
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0.5: Economical Covers With Geometric Applications - Alon, Bollobas, Kim, Vu (1999) (Correct)
0.5: Nearly-Perfect Hypergraph Packing is in NC - Grable (1996) (Correct)
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BibTeX entry: (Update)
N. Alon, H.J. Kim, J. Spencer, Nearly perfect matchings in regular simple hypergraphs, Israel Journal of Mathematics, to appear. http://citeseer.ist.psu.edu/238893.html More
@article{ alon97nearly,
author = "Alon and Kim and Spencer",
title = "Nearly Perfect Matchings in Regular Simple Hypergraphs",
journal = "IJM: Israel Journal of Mathematics",
volume = "100",
year = "1997",
url = "citeseer.ist.psu.edu/238893.html" }
Citations (may not include all citations):957 The Probabilistic Method (context) - Alon, Spencer - 1992
34 a packing and covering problem (context) - Rodl - 1985
16 Near perfect coverings in graphs and hypergraphs (context) - Frankl, Rodl - 1985
14 a limit theorem in combinatorial analysis (context) - Erdos, Hanani - 1963
7 Asymptotic packing and the random greedy algorithm (context) - Rodl, Thoma
6 Asymptotic packing via a branching process - Spencer - 1995
6 Asymptotic behaviour of the chromatic index for hypergraphs (context) - Pippenger, Spencer - 1989
5 More-than-nearly perfect packings and partial designs - Grable - 1995
4 Asymptotically Optimal Covering Designs (context) - Gordon, Kuperberg et al. - 1995
3 On self orthogonal Latin squares and partial transversals of.. (context) - Wang - 1978
1 A note on partial parallel classes in Steiner systems (context) - Lindner, Phelps - 1978
1 the size of partial parallel classes in Steiner systems (context) - Woolbright - 1980
1 has order of magnitude t 2 = ln t (context) - Kim, Number
1 the size of a maximum transversal in a Steiner Triple System (context) - Brouwer - 1981
The graph only includes citing articles where the year of publication is known.
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Asymptotic Packing via A Branching Process - Spencer (1995) (Correct)
Random Sparse Bit Strings at the Threshold of Adjacency.. - Spencer, al. (1998) (Correct)
Discrepancy in Arithmetic Progressions - Matousek, Spencer (1996) (Correct)
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