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A problem of Erdős and Sós on 3-graphs
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Glebov, Roman, Králʼ, Daniel and Volec, Jan (2016) A problem of Erdős and Sós on 3-graphs. Israel Journal of Mathematics, 211 (1). pp. 349-366. doi:10.1007/s11856-015-1267-4
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Official URL: http://dx.doi.org/10.1007/s11856-015-1267-4
Abstract
We show that for every eps > 0 there exist delta > 0 and n_0 such that every 3-uniform hypergraph on n>=n0 vertices with the property that every k-vertex subset, where k>=delta*n, induces at least (0.25+eps)*k^3/6 edges, contains K_4 as a subgraph, where K_4 is the 3-uniform hypergraph on 4 vertices with 3 edges. This question was originally raised by Erdos and Sos. The constant 0.25 is the best possible.
| Item Type: | Journal Article | ||||||
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| Subjects: | Q Science > QA Mathematics | ||||||
| Divisions: | Faculty of Science > Computer Science Faculty of Science > Mathematics |
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| Library of Congress Subject Headings (LCSH): | Extremal problems (Mathematics), Graph theory, Combinatorial analysis | ||||||
| Journal or Publication Title: | Israel Journal of Mathematics | ||||||
| Publisher: | The Hebrew University Magnes Press | ||||||
| ISSN: | 0021-2172 | ||||||
| Official Date: | February 2016 | ||||||
| Dates: |
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| Date of first compliant deposit: | 1 January 2016 | ||||||
| Volume: | 211 | ||||||
| Number: | 1 | ||||||
| Number of Pages: | 18 | ||||||
| Page Range: | pp. 349-366 | ||||||
| DOI: | 10.1007/s11856-015-1267-4 | ||||||
| Status: | Peer Reviewed | ||||||
| Publication Status: | Published | ||||||
| Access rights to Published version: | Restricted or Subscription Access | ||||||
| Funder: | Seventh Framework Programme (European Commission) (FP7), Deutsche Forschungsgemeinschaft (DFG), Univerzita Karlova. Grantové agentury (GAUK) | ||||||
| Grant number: | 259385 (FP7), 01812 (GAUK) |
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