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Constructions of non-principal families in extremal hypergraph theory
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Mubayi, Dhruv and Pikhurko, Oleg (2008) Constructions of non-principal families in extremal hypergraph theory. Discrete Mathematics, Vol.308 (No.19). pp. 4430-4434. doi:10.1016/j.disc.2007.08.040 ISSN 0012-365X.
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Official URL: http://dx.doi.org/10.1016/j.disc.2007.08.040
Abstract
A family F of k-graphs is called non-principal if its Turán density is strictly smaller than that of each individual member. For each k⩾3 we find two (explicit) k-graphs F and G such that {F,G} is non-principal. Our proofs use stability results for hypergraphs. This completely settles the question posed by Mubayi and Rödl [On the Turán number of triple systems, J. Combin. Theory A, 100 (2002) 135–152].
Also, we observe that the demonstrated non-principality phenomenon holds also with respect to the Ramsey–Turán density as well.
| Item Type: | Journal Article | ||||
|---|---|---|---|---|---|
| Subjects: | Q Science > QA Mathematics | ||||
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
| Journal or Publication Title: | Discrete Mathematics | ||||
| Publisher: | Elsevier BV | ||||
| ISSN: | 0012-365X | ||||
| Official Date: | 2008 | ||||
| Dates: |
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| Volume: | Vol.308 | ||||
| Number: | No.19 | ||||
| Number of Pages: | 5 | ||||
| Page Range: | pp. 4430-4434 | ||||
| DOI: | 10.1016/j.disc.2007.08.040 | ||||
| Status: | Peer Reviewed | ||||
| Publication Status: | Published | ||||
| Access rights to Published version: | Restricted or Subscription Access | ||||
| Funder: | NSF | ||||
| Grant number: | DMS-0400812, DMS-0457512 |
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