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Factors in random graphs
University of Gävle, Department of Mathematics, Natural and Computer Sciences, Ämnesavdelningen för matematik och statistik. (Matematik)
Department of Mathematics, Rutgers University, Piscataway, NJ, United States.
Department of Mathematics, Rutgers University, Piscataway, NJ, United States.
2008 (English)In: Random structures & algorithms (Print), ISSN 1042-9832, E-ISSN 1098-2418, Vol. 33, no 1, 1-28 p.Article in journal (Refereed) Published
Abstract [en]

Let H be a fixed graph on v vertices. For an n-vertex graph G with n divisible by v, an H-factor of G is a collection of n/v copies of H whose vertex sets partition V (G).

In this work, we consider the threshold thH(n) of the property that an Erds-Rényi random graph (on n points) contains an H-factor. Our results determine thH(n) for all strictly balanced H.

The method here extends with no difficulty to hypergraphs. As a corollary, we obtain the threshold for a perfect matching in random k-uniform hypergraph, solving the well-known Shamir's problem.

Place, publisher, year, edition, pages
2008. Vol. 33, no 1, 1-28 p.
Keyword [en]
Combinatorics, random hypergraphs
National Category
Mathematics
Identifiers
URN: urn:nbn:se:hig:diva-2056DOI: 10.1002/rsa.20224ISI: 000257500200001Scopus ID: 2-s2.0-52349115939OAI: oai:DiVA.org:hig-2056DiVA: diva2:118718
Available from: 2008-06-19 Created: 2008-06-19 Last updated: 2016-10-28Bibliographically approved

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