For a family of r-graphs F; the Tur! a an number exðn; FÞ is the maximum number of edges in an n vertex r-graph that does not contain any member of F: The Tur! a an density When F is an r-graph, pðFÞ=0; and r > 2; determining pðFÞ is a notoriously hard problem, even for very simple r-graphs F: For
The Turan Density of Triple Systems Is Not Principal
✍ Scribed by József Balogh
- Publisher
- Elsevier Science
- Year
- 2002
- Tongue
- English
- Weight
- 87 KB
- Volume
- 100
- Category
- Article
- ISSN
- 0097-3165
No coin nor oath required. For personal study only.
✦ Synopsis
The Erd + o os-Stone-Simonovits Theorem implies that the Tur! a an density of a family of graphs is the minimum of the Tur! a an densities of the individual graphs from the family. It was conjectured by Mubayi and R .
o odl (J. Combin. Theory Ser. A, submitted) that this is not necessarily true for hypergraphs, in particular for triple systems. We give an example, which shows that their conjecture is true. # 2002 Elsevier Science (USA)
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