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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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
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Science > Computer Science Faculty of Science > Mathematics
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:	Date Event February 2016 Published 26 November 2015 Available
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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