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- W72010669 abstract "The Lovasz local lemma is a powerful and well-studied probabilistic technique useful in establishing the possibility of simultaneously avoiding every event in some collection. A principle limitation of the lemma’s application is that it requires most events to be independent of one another. The lopsided local lemma relaxes the requirement of independence to negative dependence, which is more general but also more difficult to identify. We will examine general classes of negative dependent events involving maximal matchings of uniform hypergraphs, partitions of sets, and spanning trees of complete graphs. The results on hypergraph matchings (together with the configuration model of Bollobas) yield asymptotically the number of regular, uniform hypergraphs avoiding small cycles. Finally, we work toward a characterization of hypergraphs for which the matching paradigm is guaranteed generate negative dependent events." @default.
- W72010669 created "2016-06-24" @default.
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- W72010669 date "2013-01-01" @default.
- W72010669 modified "2023-09-27" @default.
- W72010669 title "Applications of the Lopsided Lovász Local Lemma Regarding Hypergraphs" @default.
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