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On the density of 2-colorable 3-graphs in which any four points span at most two edges
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
2010 (English)In: Journal of combinatorial designs (Print), ISSN 1063-8539, E-ISSN 1520-6610, Vol. 18, no 2, 105-114 p.Article in journal (Refereed) Published
Abstract [en]

Let ex(2) (n, kappa(-)(4)) be the maximum number of edges in a 2-colorable kappa(-)(4)-free 3-graph (where kappa(-)(4) ={123,124,134}). The 2-chromatic Turan density of kappa(-)(4) is pi(2)(kappa(-)(4))= lim(n ->infinity)ex(2)(n,kappa(-)(4))/ (n 3). We improve the previously best known lower and upper bounds of 0.25682 and 3/10-epsilon, respectively, by showing that 0.2572049 <= pi(2) (kappa(-)(4)) < 0.291. This implies the following new upper bound for the Turin density of kappa(-)(4) pi(kappa(-)(4)) <= 0.32908. In order to establish these results we use a combination of the properties of computer-generated extremal 3-graphs for small n and an argument based on "super-saturation". Our computer results determine the exact values of ex(n, kappa(-)(4)) for n <= 19 and ex(2)(n, kappa(-)(4)) for n <= 17, as well as the sets of extremal 3-graphs for those n. (C) 2009 Wiley Periodicals, Inc. J Combin Designs 18: 105-114, 2010

Place, publisher, year, edition, pages
2010. Vol. 18, no 2, 105-114 p.
Keyword [en]
extremal problem, hypergraph, covering design, double covering design
URN: urn:nbn:se:umu:diva-41321DOI: 10.1002/Jcd.20223ISI: 000275030700003OAI: diva2:405616
562DX Times Cited:1 Cited References Count:8Available from: 2011-03-23 Created: 2011-03-23 Last updated: 2011-03-24Bibliographically approved

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Markström, Klas
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