Journal article
On a problem of Erdős and Moser
- Abstract:
- A set A of vertices in an r-uniform hypergraph HH is covered in HH if there is some vertex u∉Au∉A such that every edge of the form {u}∪B{u}∪B , B∈A(r−1)B∈A(r−1) is in HH . Erdős and Moser (J Aust Math Soc 11:42–47, 1970) determined the minimum number of edges in a graph on n vertices such that every k-set is covered. We extend this result to r-uniform hypergraphs on sufficiently many vertices, and determine the extremal hypergraphs. We also address the problem for directed graphs.
- Publication status:
- Published
- Peer review status:
- Peer reviewed
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- Files:
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(Preview, Accepted manuscript, pdf, 264.0KB, Terms of use)
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- Publisher copy:
- 10.1007/s12188-016-0162-1
Authors
- Publisher:
- Springer Berlin Heidelberg
- Journal:
- Abhandlungen des Mathematischen Seminars der Universität Hamburg More from this journal
- Volume:
- 87
- Issue:
- 2
- Pages:
- 213–222
- Publication date:
- 2017-01-09
- Acceptance date:
- 2016-02-23
- DOI:
- EISSN:
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1865-8784
- ISSN:
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0025-5858
- Keywords:
- Pubs id:
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pubs:632958
- UUID:
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uuid:ead3e85a-741d-464c-8574-cd03e833768e
- Local pid:
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pubs:632958
- Source identifiers:
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632958
- Deposit date:
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2016-07-09
- ARK identifier:
Terms of use
- Copyright holder:
- Béla Bollobás and Alex Scott
- Copyright date:
- 2017
- Notes:
- This is an accepted manuscript of a journal article published by Springer Berlin Heidelberg in Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg on 2017-01-09, available online: http://dx.doi.org/10.1007/s12188-016-0162-1
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